Question

The sum of the ages of two persons a and b is 50. 5 years ago, the ratio of their ages was 5/3. the present age of a and b are

Answer 1

LET THE PRESENT AGE OF a BE x
AND PRESENT AGE OF b BE y
BY THE FIRST GIVEN CONDITION
x+y=50..............................................(1)

BY THE SECOND CONDITION
$\frac{x - 5}{y - 5 } = \frac{5}{3}$
3(x-5)=5(y-5)
3x-15=5y-25
3x-5y=-10................................(2)
(multiplying eqn(1) by 5 we get)
5x+5y=250...............(3).
(Adding eq no. (2) &(3))

3x-5y=-10
5x+5y=250
8x=240
x=30

substituting x=30 in equation(1)
x+y=50
30+y=50
y=20

THEREFORE, THE PRESENT AGES ARE 30 &20 yrs