Maths Class X Question Bank

Question 1 of 37

1. Question
1 point(s)
If $-4 $ is a root of the quadratic equation $x^2+px-4=0 $ and the equation $2x^2+px+k=0 $ has equal roots, find the value of $k $.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$x^2-px-4=0\\ \\ (-4)^2+(-4)p-4=0\\ \\ \Rightarrow 16-4p-4=0\\ \\ \Rightarrow 12=4p\\ \\ \Rightarrow p=3\\ \\ 2x^2+px+k=0\\ \\ \Rightarrow 2(-4)^2+3\times(-4)+k=0\\ \\ \Rightarrow 32-12+k=0\\ \\ \Rightarrow 20+k=0\Rightarrow k=-20$
Question 2 of 37

2. Question
1 point(s)
Solve for $x:4x^2-4a^2x+(a^4-b^4)=0 $.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$4x^2-4a^2x+(a^4-b^4)=0\\ \\ \Rightarrow 4x^2-a\{2(a^2+b^2)+2(a^2-b^2)\}x+(a^2-b^2)\ (a^2+b^2)=0\\ \\ \Rightarrow 4x^2-2(a^2+b^2)x-2(a^2-b^2)x+(a^2-b^2)\ (a^2+b^2)=0\\ \\ \Rightarrow 2x\{2x-(a^2+b^2)\}-(a^2-b^2)\{2x-(a^2+b^2)\}=0\\ \\ \Rightarrow 2x-(a^2-b^2)=0\ \text{or}\ 2x-(a^2+b^2)=0\\ \\ \Rightarrow x=\dfrac{a^2-b^2}{2},\dfrac{a^2+b^2}{2}$
Question 3 of 37

3. Question
1 point(s)
Solve for $x:16x^2-8a^2x+(a^4-b^4)=0 $.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$16x^2-8a^2x+(a^4-b^4)=0\\ \\ (16x^2-8a^2x+a^4)-b^4=0\\ \\ (a^2-4x)^2-b^4=0\\ \\ (a^2-4x+b^2)\ (a^2-4x-b^2)=0\\ \\ a^2-4x+b^2=0,\ a^2-4x-b^2=0\\ \\ \Rightarrow x=\dfrac{a^2+b^2}{4},x=\dfrac{a^2-b^2}{4}$
Question 4 of 37

4. Question
1 point(s)
The difference of the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Find the numbers.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let the larger number be $x$
Square of the smaller number $=4x$
Square of the larger number $x^2$
A/Q $x^2-4x=45$
$\Rightarrow x^2-4x-45=0\\ \\ \Rightarrow x(x-9)+5(x-9)=0\\ \\ \Rightarrow x=-5,9$
square of smaller number $=4x=4\times9=36$
smaller number $=\pm6$
The numbers are 9 and 6 or 9 and -6
Question 5 of 37

5. Question
1 point(s)
Out of a number of Saras birds, one fourth the number are moving about in lotus plants, $\dfrac{1}{9} $th coupled (along) with $\dfrac{1}{4} $ as well as 7 times the square root of the number move on a hill, 56 birds remain in Vakula trees. What is the total number of birds ?
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let the number of saras birds be $x$
No. of birds moving about in lots $=\dfrac{x}{4}$
A/Q $\dfrac{x}{4}+\dfrac{x}{4}+\dfrac{x}{9}+7\sqrt x+56=x$
$\Rightarrow \dfrac{y^2}{4}+\dfrac{y^2}{4}+\dfrac{y^2}{9}+7y+56=y^2(\because x=y^2)\\ \\ \Rightarrow 9y^2+9y^2+4y^2+252y+2016=36y^2\\ \\ \Rightarrow 14y^2-252y-2016=0\\ \\ \Rightarrow 7y^2-126y-1008=0\\ \\ \Rightarrow y^2-24y+6y-144=0\\ \\ \Rightarrow y=-6,24$
No. of saras birds $=x=y^2=24^2=576$
Question 6 of 37

6. Question
1 point(s)
A train, travelling at a uniform speed for 360 km, would have taken 48 minuts less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let original speed $=x$ km/hr
A/Q $\dfrac{360}{x}-\dfrac{360}{x+5}=\dfrac{48}{60}=\dfrac{4}{5}$
$\Rightarrow 360\left[\dfrac{1}{x}-\dfrac{1}{x+5}\right]=\dfrac{4}{5}\\ \\ \Rightarrow x^2+5x-2250=0\\ \\ \Rightarrow x^2+50x-45x-2250=0\\ \\ \Rightarrow x=-50,45$
original speed $=45$ km/hr
Question 7 of 37

7. Question
1 point(s)
If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let age of zeba $=x$ years
$(x-5)^2=11+5x\\ \\ \Rightarrow x^2+25-10x=11+5x\\ \\ \Rightarrow x^2-15x+14=0\\ \\ \Rightarrow x=1,\ 14$
her age will be 14 years becomes if she was 1 year old the 5 years younger cannot happen
Question 8 of 37

8. Question
1 point(s)
A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let speed of boat in still water $=x$ km/hr
A/Q $\dfrac{8}{x+2}+\dfrac{8}{x-2}=\dfrac{5}{3}$
$\Rightarrow 24(x-2)+24(x+2)=5(x+2)\ (x-2)\\ \\ \Rightarrow 48x=5x^2-20\\ \\ \Rightarrow 5x^2-48x-20=0\\ \\ \Rightarrow x=\dfrac{48+\sqrt{(-48)^2-4\times5\times(-20)}}{10}\\ \\ =\dfrac{48+52}{10}=\dfrac{100}{10}=10$
Question 9 of 37

9. Question
1 point(s)
Out of a group of swans, 7/2 times the square root of the total number are playing on the shore of a pond. The two remaining ones are swinging in water. Find the total number of swans.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let total number of swans $=x$
A/Q $x=\dfrac{7}{2\sqrt x}+2$
$\Rightarrow x-2=\dfrac{7}{2}\sqrt x\\ \\ \Rightarrow 2(x-2)=7\sqrt x\\ \\ \Rightarrow 4(x-2)^2=49x\\ \\ \Rightarrow 4x^2-65x+16=0\\ \\ \Rightarrow (x-16)\ (4x-1)=0\\ \\ \Rightarrow x=16,\dfrac{1}{4}$
No. of swans $=16$
Question 10 of 37

10. Question
1 point(s)
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let present age of first friend $=x$
second friend $=20-x$
A/Q $(x-4)(16-x)=48$
$\Rightarrow 16x-x^2-64+4x=48\\ \\ \Rightarrow -x^2+20x-112=0\\ \\ \Rightarrow x^2-20x+112=0\\ \\ D=b^2-4ac=(-20)^2-4\times1\times112\\ \\ =400-448=-48$
Since $D>0$ , the equation has no real roots.
Hence the given situation is not possible.
Question 11 of 37

11. Question
1 point(s)
Three consecutive positive integers are taken such that the sum of the square of the first and the product of the other two is 154. Find the integers.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let three consecutive integer be $x,x+1,x+2$
A/Q $x^2+(x+1)\ (x+2)=154$
$\Rightarrow x^2+x^2+2x+x+2=154\\ \\ \Rightarrow 2x^2+3x-152=0\\ \\ \Rightarrow 2x^2-16x+19x-152=0\\ \\ \Rightarrow 2x(x-8)+19(x-8)=0\\ \\ \Rightarrow x=\dfrac{-19}{2},8$
Integers are 8, 9, 10
Question 12 of 37

12. Question
1 point(s)
The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return downstream to the original point in 2 hrs 45 min. Find the speed of the stream.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let speed of stream $=x$ km/hr
speed of boat downstream $=(x+11)$ km/hr
speed of boat upstream $=(11-x)$ km/hr
A/Q $\dfrac{12}{11+x}+\dfrac{12}{11-x}=2\dfrac{45}{60}$
$\Rightarrow \dfrac{12\times22}{121-x^2}=\dfrac{11}{4}\\ \\ \Rightarrow 121-x^2=96\Rightarrow x^2=25=\pm5$
Speed of stream $=5$ km/hr
Question 13 of 37

13. Question
1 point(s)
The product of the digits of a two digit positive number is 24. If 18 is added to the number, then the digits of the number are interchanged. Find the number.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let ten’s digit $=x$
Unit’s digit $=\dfrac{24}{x}$
Number $=10x+\dfrac{24}{x}$
A/Q $10x+\dfrac{24}{x}+18=10\times\dfrac{24}{x}+x$
$\Rightarrow 10x^2+24+18x=240+x^2\\ \\ \Rightarrow 9x^2+18x=216\\ \\ \Rightarrow x^2+2x-24=0\\ \\ \Rightarrow x^2+6x-4x-24=0\\ \\ \Rightarrow x=-6,4\Rightarrow \ x=4$
No. $=10x+\dfrac{24}{x}=10\times4+\dfrac{24}{4}=46$
Question 14 of 37

14. Question
1 point(s)
Two taps together can fill a tank in $9\dfrac{3}{8} $ hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let the tap with smaller diameter fills in $x$ hours and larger diameter fills in $(x-10)$ hours
A/Q $\dfrac{1}{x}+\dfrac{1}{x-10}=\dfrac{8}{75}$
$\Rightarrow 75(2x-10)=8(x^2-10x)\\ \\ \Rightarrow 150x-750=8x^2-80x\\ \\ \Rightarrow 4x^2-115x+375=0\\ \\ \Rightarrow (4x-15)(x-25)=0\ \Rightarrow x=\dfrac{15}{4},25$
The tap of smaller diameter can fill in 25 hours and larger in (25 – 10) = 15 hours
Question 15 of 37

15. Question
1 point(s)
A train travels at a uniform speed for a distance of 63 km and then travels a distance of 72 km at an aveage speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is the original speed of the train?
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let original speed $=x$ km/hr
A/Q $\dfrac{63}{x}+\dfrac{72}{x+6}=3$
$\Rightarrow 63(x+6)+72x=3x(x+6)\\ \\ \Rightarrow 45x+21\times6=x^2+6x\\ \\ \Rightarrow x^2-39x-126=0\\ \\ \Rightarrow x^2-42x+3x-126=0\\ \\ \Rightarrow x=42,-3$
original speed $=42$ km/hr
Question 16 of 37

16. Question
1 point(s)
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let larger number $=x$
Smaller number $=\pm\sqrt{8x}$
A/Q $x^2-(\sqrt{8x})^2=180$
$x^2-8x-180=0\\ \\ x^2+10x-18x-180=0\\ \\ x(x+10)-18(x+10)=0\\ \\ x=18,-10$
Smaller number $=\pm\sqrt{8x}=\pm\sqrt{8\times18}=\pm12$
Number are 18 and 12 and 18 and -12
Question 17 of 37

17. Question
1 point(s)
Two pipes running together can fill a tank in 6 minutes. If one pipe takes 5 minutes more than the other to fill the tank, find the time in which each pipe would fill the tank separately.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let the taken to fill the cutan
Let $x$ and $(x+5)$ min respectively
A/Q $\dfrac{1}{x}+\dfrac{1}{x+5}=\dfrac{1}{6}$
$\Rightarrow 2x+\dfrac{5}{x^2}+5x=\dfrac{1}{6}\\ \\ \Rightarrow x^2-7x-30=0\\ \\ \Rightarrow x^2-10x+3x-30=0\\ \\ \Rightarrow (x-10)(x+3)=0\\ \\ \Rightarrow x=10,-3$
So $x=10$ and $x+5=10+5=15$ min
Question 18 of 37

18. Question
1 point(s)
A motorboat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of stream.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Speed of boat in still water = 18 km/hr
Speed of stream $=x$ km/hr
A/Q $\dfrac{24}{18-x}-\dfrac{24}{18+x}=1$
$\Rightarrow \dfrac{432+24x-432+24x}{(18-x)(18+x)}=1\\ \\ \Rightarrow 48x=324-x^2\\ \\ \Rightarrow x^2+48x-324=0\\ \\ \Rightarrow x^2+54x-6x-324=0$
$\Rightarrow x=-54,6$ speed of stream $=6$ km/hr
Question 19 of 37

19. Question
1 point(s)
A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train was 10 km/hr less than that of the fast train, find the speed of the trains.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let speed of slow train be $x$ km/hr and fast train be $(x+10)$ km/hr
A/Q $\dfrac{600}{x}-\dfrac{600}{x+10}=3$
$\Rightarrow \dfrac{600x+6000-600x}{x(x+10)}=3\\ \\ \Rightarrow \dfrac{6000}{x(x+10)}=3\\ \\ \Rightarrow 2000=x^2+10x\\ \\ \Rightarrow x^2+10x-2000=0\\ \\ \Rightarrow x^2+50x-40x-2000=0\\ \\ \Rightarrow x^2+50x-40x-2000=0\\ \\ \Rightarrow x=40,-50$
Speed of slow train = 40 km/hr and fast train = 50 km/hr
Question 20 of 37

20. Question
1 point(s)
Two pipes can together fill a tank in $3\dfrac{1}{13} $ minutes.
If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe can fill the tank.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let one pipe fills the cetrain in $x$ minutes and other in $(x+3)$ minutes
A/Q $\dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{13}{40}$
$\Rightarrow \dfrac{2x+3}{x^2+3x}=\dfrac{13}{40}\\ \\ \Rightarrow 13x^2-41x-120=0\\ \\ \Rightarrow 13x^2-65x+24x-120=0\\ \\ \Rightarrow x-5=0,\ 13x+24=0\\ \\ \Rightarrow x=5,\dfrac{-24}{13}$
one pipe will take 5 min and other will take (5+3) = 8 min
Question 21 of 37

21. Question
1 point(s)
By increasing the speed of a bus by 10 km/hr, it takes one and half hours less to cover a journey of 450 km. Find the original speed of the bus.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let speed of bus be $x$ km/hr
A/Q $\dfrac{450}{x}-\dfrac{450}{x+10}=\dfrac{3}{2}$
$\Rightarrow 450(x+10)-450x=\dfrac{3}{2}(x^2+10x)\\ \\ \Rightarrow x^2+10x-3000=0\\ \\ \Rightarrow x^2+60x-50x-3000=0\\ \\ \Rightarrow x=-60,50\\ \\ \Rightarrow x=50$ as $-60$ is not possible.
Question 22 of 37

22. Question
1 point(s)
The hypotenuse of a right triangle is $3\sqrt5 $ cm. If the smaller side is tripled and the larger side is doubled, the new hypotenuse will be 15 cm. Find the length of each side.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let smaller side be $x$ cm and larger side be $y$ cm
A/Q $x^2+y^2=(3\sqrt5)^2$
$\Rightarrow x^2+y^2=45$ …(3)
Also $(3x)^2+(2y)^2=(15)^2$
$\Rightarrow 9x^2+4y^2=225$ …(2)
Solving (1) and (2)
$9x^2+4(45-x^2)=225\\ \\ \Rightarrow 5x^2=225-180\\ \\ \Rightarrow 5x^2=45\\ \\ \Rightarrow x=\pm3\\ \\ 9+y^2=45\Rightarrow y^2=36\Rightarrow y=\pm6$
Length of the smaller side = 3 cm and longer side = 6 cm
Question 23 of 37

23. Question
1 point(s)
A man bought a certain number of toys for Rs 180. He kept one for his own use and sold the rest for one rupee each more than he gave for them. Besides getting his own toy for nothing, he made a profit of Rs 10. Find the number of toys, he initially bought.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let number of toys $=x$
cost of 1 toy $=\dfrac{180}{x}$
A/Q $SP=\dfrac{180}{x}+1$
SP of $(x-1)$ toys $=\left(\dfrac{180}{x}+1\right)(x-1)$
Profit = SP – CP
$\Rightarrow \left(\dfrac{180}{x}+1\right)(x-1)-180=10\\ \\ \Rightarrow (180+x)\ (x-1)=190x\\ \\ \Rightarrow (x-20)\ (x+9)=0\Rightarrow x=20,-9$
Number of toys = 20
Question 24 of 37

24. Question
1 point(s)
A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let usual speed be $x$ km/hr
New speed $=(x+250)$ km/hr
$\dfrac{1500}{x}-\dfrac{1500}{x+250}=\dfrac{30}{60}\\ \\ \Rightarrow \dfrac{1500x+1500\times250-1500x}{x^2+250x}=\dfrac{1}{2}\\ \\ \Rightarrow 750000=x^2+250x\\ \\ x^2+250x-750000=0\\ \\ \Rightarrow x=750,\ -1000$
usual speed of the plane = 750 km/hr
Question 25 of 37

25. Question
1 point(s)
A train travels 300 km at a uniform speed. If the speed of the train had been 5 km/hour more, it would have taken 2 hours less for the same journey. Find the usual speed of the train.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let constant speed $=x$ km/hr
A/Q $\dfrac{300}{x}-\dfrac{300}{x+5}=2$
$\Rightarrow \dfrac{300x+1500-300x}{x^2+5x}=2\\ \\ \Rightarrow x^2+5x-750=0\\ \\ \Rightarrow x^2+30x-25x-750=0\\ \\ \Rightarrow x=-30,25$
original speed = 25 km/hr
Question 26 of 37

26. Question
1 point(s)
The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let speed of stream $=x$ km/hr
A/Q $\dfrac{30}{15-x}+\dfrac{30}{15+x}=\dfrac{9}{2}$
$\Rightarrow 30\left(\dfrac{30}{225-x^2}\right)=\dfrac{9}{2}\\ \\ \Rightarrow 225-x^2=\dfrac{30\times30\times2}{9}\\ \\ \Rightarrow 225-x^2=200\ \Rightarrow x=\pm5$
speed of the stream 5 km/hr
Question 27 of 37

27. Question
1 point(s)
The sum of ages of father and his son is 45 years. 5 years ago, the product of their ages was 124. Determine their present ages.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$(x-5)(40-x)=124\\ \\ \Rightarrow x^2-45x+324=0\\ \\ \Rightarrow (x-9)(x-36)=0\\ \\ \Rightarrow x=9,36$
The present age of son is 9 years and father is 36 years.
Question 28 of 37

28. Question
1 point(s)
The numerator of a fraction is 3 less than its denominator. If 2 is addd to both numerator as well as denominator, the sum of new and original fraction is $\dfrac{29}{20} $, find the frction.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$\dfrac{x-3}{x}+\dfrac{x-1}{x+2}=\dfrac{29}{20}\\ \\ \Rightarrow 20[(x-3)(x+2)+x(x-1)]=29(x^2+2x)\\ \\ \Rightarrow 20[2x^2-2x-6]=29x^2+58x\\ \\ \Rightarrow 11x^2-9x-120=0\\ \\ \Rightarrow x=10,\dfrac{-11}{12}$
The fraction is $\dfrac{7}{10}$
Question 29 of 37

29. Question
1 point(s)
The hypotenuse of a right angled triangle is 6 cm more than twice its shortest side. If third side is 2 cm less than the hypotenuse, find the sides of this triangle.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let length of shortest side $=x$ m
hypotenuse $=2x+6$
Third side $=2x+4$
$(2x+6)^2=x^2+(2x+4)^2\\ \\ \Rightarrow x^2-8x-20=0\\ \\ \Rightarrow (x-10)\ (x+2)=0\Rightarrow x=10,-2$
Sides are 10m, 24m, 26m
Question 30 of 37

30. Question
1 point(s)
The differene of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let two numbers be $a$ and $b$
$a^2-b^2=45$ …(1)
$b^2=4a$ …(2)
on solving two equation we get
$a=9,-5$
If $a=-5,\ b^2=20$
If $a=9,\ b^2=36,\ b=\pm6$
Numbers are 9, 6 or 9, -6
Question 31 of 37

31. Question
1 point(s)
The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is $2\dfrac{16}{21} $, find the fraction.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$\dfrac{x}{2x+1}+\dfrac{2x+1}{x}=\dfrac{58}{21}\\ \\ \Rightarrow \dfrac{x^2+(2x+1)^2}{x(2x+1)}=\dfrac{58}{21}\\ \\ \Rightarrow \dfrac{5x^2+4x+1}{2x^2+x}=\dfrac{58}{21}\\ \\ \Rightarrow 11x^2-26x-21=0\Rightarrow x=3,\dfrac{-7}{11}$
Fraction $=\dfrac{3}{7}$
Question 32 of 37

32. Question
1 point(s)
In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in Maths and 4 marks less in Science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$(x+3)(y-4)=180$ …(1) and $x+y=28$ …(2)
$(x+3)(24-x)=180\\ \\ \Rightarrow x^2-21x+108=0\\ \\ \Rightarrow x=12,9\Rightarrow y=16,9$
P obtained 12 marks in mathematics and 16 in science or P obtained 9 marks in mathematics and 19 in science
Question 33 of 37

33. Question
1 point(s)
A peacock is sitting on the top of a pillar which is 9 m high. From a point 27 m away from the bottom of the pillar, a snake is coming to its hole at the base of pillar. Seeing the snake the peacock pounces on it. If their speeds are equal, at what distance from the hole is the snake caught?
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$x^2=9^2+(27-x)^2\\ \\ \Rightarrow x^2=81+729-54x+x^2\\ \\ \Rightarrow x=15$
The snake is caught at (27 – 15) = 12m
Question 34 of 37

34. Question
1 point(s)
In a class test the sum of Gagan’s, marks in Mathematics and English is 45. If he had 1 more mark in Maths and 1 less in English, the product of marks would have been 500. Find the original marks obtained by Gagan in Maths and English separately.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$(x+1)(45-x-1)=500\\ \\ \Rightarrow (x+1)(44-x)=500\\ \\ \Rightarrow x^2-43x+456=0\\ \\ \Rightarrow x=19,24$
Question 35 of 37

35. Question
1 point(s)
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$5x-5y=100\\ \\ \Rightarrow x-y=20\\ \\ x+y=100$
on solving $x=60, y=40$
speed of car at A = 60 km/hr, B = 40 km/hr
Question 36 of 37

36. Question
1 point(s)
A trader bought a number of articles for Rs 900, five articles were found damaged. He sold each of the remaining articles at Rs 2 more than what he paid for it. He got a profit of Rs 80 on the whole transaction. Find the number of articles he bought.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

Let no. of articles be $n$
$(n-5)\times(a+2)=900+980\\ \\ na-5a+2n-10=980\\ \\ 2n-\dfrac{4500}{n}=90\\ \\ \Rightarrow n^2-2250=45n\Rightarrow n=75,-30$
Hence no. of articles = 75
Question 37 of 37

37. Question
1 point(s)
Two years ago a man’s age was three times the square of his son’s age. Three years hence his age will be four times his son’s age. Find their present ages.
- Upload your answer to this question.
  
  This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Grading can be reviewed and adjusted.

Grading can be reviewed and adjusted.

Hint

$(x-2)=3(y-2)^2\\ \\ (x+3)=4(y+3)\\ \\ x+3=4y+12\Rightarrow x=4y+9$
on solving $y=5,\dfrac{1}{3}$
son’s age = 5 years, father’s age = 29 years