Question

Q41. The ratio of ages of A and B 4 years ago was 5:3. The sum of present ages of A, B and C is 80
years. If present age of C is equal to sum of present ages of A and B. find the present age of A.
(a) 17 years
(b) 24 years
(c) 20 years
(d) 22 years
(e) 18 years​

Answer 1

Answer:

If the ratio of age of A to the age of B four years ago was 5:3 and the sum of present ages of A, B and C is 80 and if the present age of C is the sum of ages of A and B, then the present age of A is 24 years

Step-by-step explanation:

Let us take a, b, and c as the present ages of A, B, and C respectively.

Given that

The ratio of ages of A and B four years ago = 5:3

That is if (a-4) = 5x, then ( b-4) = 3x

That is a = 5x+4 and b= 3x+4

Given that a+b+c =80

Also c = a+b

Then a+ b+ c = a+ b+ a+b

That is 2(a+b) = 80

a+b = 80/2 = 40

Given a + b =40

a= 5x+4 and b= 3x+4

Substitute the values

That is a+b = 5x+4+3x+4

= 8x+ 8

= 8(x+1)

Then 8(x+1) = 40

x+1 = 40/8

x+1=5

x=5-1

x=4

Then the age of A = a = 5x+4

=( 5*4)+4 = 20+4=24

Therefore the age of A is 24 years