Question

4. Three years ago, the average age of A, B and C was 27 years and that of Band C 5 years ago was
20 years. A's present age is
(a) 30 years
(b) 35 years
(C) 40 years
(d) 48 years​

Answer 1

Answer:

present age of B is 25

present age of C is 25

so

average age of A, B and C in present is

A+B+C/3=27+3

A+25+25/3=30

A+50/3=30

A+50=90

A=90-50

A=40

A's present age is 40

Answer 2

Let's consider the present age of A to be  ⇒ x

Let's consider the present age of B to be  ⇒ y

Let's consider the present age of C to be ⇒ z

Age of A, B and C, 3 years ago would be ⇒

Age of A, 3 years would be ⇒ x-3

Age of B, 3 years would be ⇒ y-3

Age of C, 3 years would be ⇒ z-3

Average age of A, B and C, three years ago ⇒ 27

Formula for average ⇒ $\dfrac{Sum\ of \ all \ Observations }{Number \ of \ Observation }$

Therefore we must simplify this equation ⇒ $\dfrac{(x-3)+(y-3)+(z-3)}{3} = 27$

⇒ $x+y+z=27\times 3 + 9 = 90$ (1)

Ages of A, B and C, 5 years ago would have been ⇒

Age of B, 3 years would be ⇒ y-5

Age of C, 3 years would be ⇒ z-5

Average age of B and C, five years ago ⇒ 20

Formula for average ⇒ $\dfrac{Sum\ of \ all \ Observations }{Number \ of \ Observation }$

Therefore we must simplify this equation ⇒ $\dfrac{(y-5)+(z-5)}{2}=20$

⇒ $y+z=50$ (2)

From (1) and (2) we must subtract them to find the A's present age.

90 - 50 = 40

∴ The present age of A is (c) 40 years