Question

If The Ratio Of The Ages Of A and B , 5 Years Ago Was 5:7 Then Which Of The Following Can Be The Sum Of Their Ages 5 years From Now

A) 90
B) 98
C) 92
D) 87

Answer 1

Given that:

Ratio of ages of A and B, 5 years ago was 5 : 7

So, we can let the age of A, 5 years ago = 5$x$ and

The age of B, 5 years ago = 7$x$

To find:

The sum of their ages 5 years from now can be:

A) 90

B) 98

C) 92

D) 87

Solution:

The present ages of A and B will be equal to their ages 5 years ago plus 5.

i.e. 5$x$+5 and 7$x$+5 respectively.

The ages of A and B after 5 years will be:

Their present ages plus 5

i.e.

5$x$+10 and 7$x$+10 respectively.

Now, the sum is:

5$x$+10 + 7$x$+10 = 12$x$+20

Now, checking the options one by one:

A) 12$x$+20 = 90 $\Rightarrow 12x = 70$

$x$ not an integer.

so A) is false.

B) 12$x$+20 = 98 $\Rightarrow 12x = 78$

$x$ not an integer.

so B) is false.

C) 12$x$+20 = 92 $\Rightarrow 12x = 72$

$x$ = 6.

so C) is True.

So, sum of their ages can be: C) 72

Answer 2

Answer:

So  n  is the sum of the ages 5 years from now. Hence the sum of ages today must be  n−10 . (Subtracting 5 years for each of the two)

Today their ages are in the ratio  5:7 , so we can split the sum  (n−10)  into two number satisfying this ratio, which are -

512(n−10)  and  712(n−10)  

Observe that if you add these two, you get sum  (n−10)  and if you take their ratio you get  5:7 . But for these to give you two integers,  (n−10)  must be divisible by  12 . So here is what you need to check

Subtract  10  from each answer option  n , to get  (n−10)  

Check which of these  (n−10)  are divisible by 12.

Hopefully only one of the given answer option satisfy this.