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Parin Sir > Quantitative Aptitude (Maths) > Linear Equations > Examples 11 to 15 > Examples 11 to 15

Examples 11 to 15

July 19, 2020
Category: Examples 11 to 15

(11) A father is now five times as old as his son. Five years ago, he was nine times as old as his son. Find their present ages.

Soln. Let age of the father = x and that of the son = y

We are given that, x = 5y –––––––––– ( 1 )

& ( x – 5 ) = 9 ( y – 5 ) $\large \Rightarrow$ x – 9y = – 40 –––––––––––– ( 2 )

Solving eq. ( 1 ) and ( 2 ), we get x = 50 and y = 10

(12) If 5 years ago the sum of father’s age and his two sons’ age is 110 years, then the sum of their ages 10 years from today would be :

Soln.

(13) If Radha buys 5 T- shirts and 3 jeans for Rs. 9500 and 4 T-shirts and 2 jeans for Rs. 6800, how much does she need to buy 3 T-shirts and 2 jeans ?

Soln. Let the T-shirt cost = Rs. x and Jeans cost = Rs. y.

5x + 3y = 9500 ––– ( 1 )

4x + 2y = 6800 ––– ( 2 )

Solving equation ( 1 ) and ( 2 ), we get x = 700 $\therefore$ y = 2000

Hence, 3 T-shirts and 2 jeans will cost her 3 ( 700 ) + 2 ( 2000 ) = Rs. 6100

(14) Solve for x, y, z : 3x + 2y = 13, 5y + 3z = 22 and 2x + z = 10.

Soln. Here, 3x + 2y = 13 ––– ( 1 )

5y + 3z = 22 ––– ( 2 )

and 2x + z = 10 ––– ( 3 )

Eliminating eq. ( 1 ) and ( 2 ), we get

5x – 2z = 7 ––– ( 4 )

Solving equation ( 3 ) and ( 4 ), we get x = 3 and z = 4

Substituting the value of x = 3, we get y = 2

(15) A man employs 5 men, 4 women and ‘x’ children. He pays daily wages of Rs. 150 per man, Rs. 120 per women and Rs. 80 per child. His average bill for the day works out to Rs. 105.50 per person. What is the value of ‘x’ ?

Soln. Here, n₁ = 5, n₂ = 4, n₃ = x, $\overline{x}_{1}$ = Rs. 150, $\overline{x}_{2}$ = Rs. 120 & $\overline{x}_{3}$ = Rs. 80