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Hitasha is four years older than her friend Sulekha. Hitasha’s mother is twice as old as Hitasha and Sulekha is twice as old as her brother. The age of Hitasha’s mother is 41 years more than the age of Sulekha’s brother. Find the age of Hitasha and Sulekha.
Let the ages of Hitasha and Sulekha be x and y years respectively.
y+x=4
Hitasha’s mother(z)=2x
Sulekha’s brother
Solve by the method of cross multiplication
\(\begin{array}{l}5x – 8y – 58 = 0\\3x + 9y – 21 = 0\end{array}\)
On selling a holder box at 40% gain and bowl at 50% gain a seller gains Rs16. If he sells the holder box at 40% gain and bowl box at 70% gain he gains Rs22. Find the actual price of holder box and bowl box.
Similarly,
Solving 2 equations we get x=2.5, y=30
Solve the following system of equations by the method of substitution.
\(\begin{array}{l}\left( {m – n} \right)x + \left( {m + n} \right)y = {m^2} + {n^2}\\\left( {m + n} \right)x + \left( {m – n} \right)y = {m^2} + {n^2}\end{array}\)
Put this value of x in equation (2),
On solving we get
Points P and Q are 44km apart on a highway. A car starts from P and another car starts from Q at the same time. If they travel in the same direction they meet in 4 hours. But if they travel towards each other they meet in one hour. What are their speeds?
Adding equations (1) and (2),
x=16.5Km/hr, y=27.5Km/hr
If the length of a rectangle is increased by 22 units and its breadth is decreased by 11 units then the area of the rectangle is increased by 55 square units. However if we decrease its length by 11 units and increase breadth by 5 units. Its area is decreased by 275 square units. Find the length and breadth of the rectangle.
Let the length be x and breadth be y. Area =xy
According to question,
Solving 2 equations we get, x=143, y=85
If a two digit number, its unit’s length is 3 more than ten’s digit. If sum of this number and the number obtained by reversing the order of its digits is 143. Find the number.
Let the ten’s digit be x
Unit’s digit be x+3
Number=10x+x+3=11x+3
Number obtained by reversing the digit
According to question,
Number is 58.
It is given the sum of the digits of a two digit number is 10. If 54 is added to the number the digits interchange their place. Find the number.
x+y=10…(1)
On solving 2nd equations,
Number is 28.
Solve the following system of linear equations by equating the coefficient.
\(\begin{array}{l}\dfrac{7}{x} + \dfrac{8}{y} = 402\\\dfrac{5}{x} + \dfrac{6}{y} = 298\end{array}\)
Solving equation (3) and equation (4),
Solve the following pair by the method of cross multiplication.
\(\begin{array}{l}\dfrac{x}{g} + \dfrac{y}{h} = g + h\\\dfrac{x}{{{g^2}}} + \dfrac{y}{{{h^2}}} = 0\end{array}\)
Rohit went to withdraw Rs.8500 from the bank. He asked the cahier to give Rs.500 and Rs.1000 notes only. Rohit got 12 notes in all. Find the number of Rs.500 and Rs.1000 notes he received.
Let the notes of Rs500 be x and Rs1000 be (12x)
It is given that the sum of digits of a two digit number is 8. If 36 is added to the number, the digits interchange their place. Find the number.
Solving 2 equations we get
The number is 26.
If thrice the daughter’s in years is added to mother’s age the sum is 66. If thrice the mother’s age is added to the daughter’s age the sum is 110. Find the age of mother and daughter.
Let the daughter’s age be x and mother’s age be y.
According to question,
On solving x=11, y=33
The value of k for which the equation \(x – 7y = 4\) and\(2x = ky = 8\) has a unique solution is
Find the value of k for which two equations \( – 3p + kq + 1 = 0\) and \( – 3p + q – 2 = 0\) will have no solution.
Find the value of k such that equations \( – 6p – 3q – 6 = 0\) and \( – 2p + kq – 2 = 0\) represents coincident lines.
Two years ago Archana was four times older than her daughter. After two years Archana will be four years more than two times the age of her daughter. Find the present age of Archana and her daughter.
Let the present age of Archana be x and daughter be y years respectively.
According to question,
Solving equation (1) and (2) we get, x=18, y=6
If 6 is added to the numerator and denominator of a dfraction, the dfraction becomes \(\dfrac{{27}}{{31}}\)and if 2 is subtracted from its numerator and denominator it becomes \(\dfrac{{19}}{{23}}\). Find the dfraction.
Solving equation (1) and (2) we get,
x=21, y=25
The ratio between the two digits number and the sum of its digits of that number is 4:1. If the digit in the unit place is 3 more than the digit in the tenth place. What is the number?
Let the ten’s place be x,
Solving 2 equations,
Number is 36.
The value of k for which the system of equations \(x+2y−3=0\) and \(5x+ky+7=0\) has no solution is
Value of x in pair of linear equations. \(170x−396y=169\) and \(396x+170y=−735\) is
Solving 2 equations we get,
The value of k for which the system of equations \(5x+2y=0\) and \(kx+20y=0\) has a nonzero solution
The value of k for which the system of equations \(x+ky+30=0\) and \(5x+30y−150=0\) represent parallel lines is
Solve for \(x \text{and} \ y\)
\(\begin{array}{l}\dfrac{{50}}{{x – y}} + \dfrac{{66}}{{x + y}} = 30\\\dfrac{{60}}{{x – y}} + \dfrac{{77}}{{x + y}} = 33\end{array}\)
Let
On solving we get,
Subtracting equation (3) from (4),
The denominator of a rational number is greater than its numerator by 4. If 4 is subtracted from the numerator and 6 is added to the denominator, the new number becomes \(\dfrac{1}{4}\). The original number was
Let the numerator be x
Denominator by x+4