Question

The difference of the present age of a and b is 10 years. If 8 years back their ages were in the ratio of 4:3, what is the average age of a and b at present?
(a) 36 years
(b)38 years
(c)41 years
(d)43 years

Answer 1

the average age of a and b is (D) 43 years

Answer 2

The average age of a and b is 33 yrs.

Step-by-step explanation:

Since we have given that

$a-b=10\ yrs$ ------------------------(1)

8 years ago,

Age of a was = $a-8$

Age of b was = $b-8$

Ratio of a to b = 4:3

According to question, we get that

$\dfrac{a-8}{b-8}=\dfrac{4}{3}\\\\3(a-8)=4(b-8)\\\\3a-24=4b-32\\\\3a-4b=-32+24\\\\3a-4b=-8-------------------(2)$

From eq(1) and eq(2), we get that

$3a-4b=-8\\\\3a-3b=30\\\\--------------------------------\\\\-a=-38\\\\a=38\ yrs$

So, the age of b would be

$a-b=10\\\\38-b=10\\\\38-10=b\\\\28=b$

So, the average age of a and b would be

$\dfrac{38+28}{2}=\dfrac{66}{2}=33\ yrs$

Hence, the average age of a and b is 33 yrs.

# learn more:

The total of the ages of Jayant, Prem and

Saransh is 93 years. Ten years ago, the ratio of

their ages was 2 : 3 : 4. What is the present age

of Saransh?

(a) 44 years (b) 36 years

(c) 33 years (d) 38 years

https://brainly.in/question/8407848