Aptitude - Average - Discussion

Just find their present ages.

h + w + c /3 = 27.
h + w + c = 27 × 3 = 81.
(But this total sum was 3 years ago, to find today's total sum, add 3 years of husband, wife and child in 81, 3 + 3 + 3 =9).

h + w + c =81 + 9 = 90 -----> A.

In the same way,
w + c /2 = 20
w+c = 40 ( but it was 5 years ago, so add 5 to both wife and child total of 10).

w + c = 40 + 10 =50 ------> B
We got our A and B equations; if we combine them, we will find our answer.

h + 50= 90 ( we have put equation B in A),
h = 90 - 50,
h = 40,
So, the husband's age is 40.

The average of H, W, C = 27.
Total age 3 years ago = 27 × 3 = 81
and average of W, C = 20.
Total age 5 years ago = 20 × 2 = 40.

Convert to the present age equation.
(H-3) +( W -3)+ (C-3 )= 81.
H + W + C - 9 = 81
H + W + C = 90 ---> 1

(W-5) + (C - 5) = 40.
W + C - 10 = 40
W + C = 50 ---> 2.

Subtract to find H from equ 1 & 2.

Then H = 90 − 50 = 40.

As per statement.

SCENARIO 1 :

The average age of husband, wife and their child - 3 years ago was 27 years.

3 yrs ago was 27 means now = 30 (27+3),
therefore AVERAGE AGE =(H+W+C)/3=30,
By simplifying equation : (H+W+C)=90.

SCENARIO 2:
Wife and the child 5 years ago was 20 years
5YRS ago means now = 25 (20+5).

therefore average = (W+C)/2=25.
By simplifying equation : (W+C)=50.
W=50-C.

Now considering and subtituting in

SCENARIO 1# i.e

(H+W+C) = 90,
H+50-C+C = 90,
H+50 = 90,
H = 90-50,
H = 40.

HENCE B=40 IS The answer.

Present age average of H+W+C,

(H+W+C)/3 =30 ,since 27 + after 3 years.
=> H+W+C= 90(equation 1)

Present age average of Wife and Child,
(W+C)/2= 25(since 20+ 5 additional years),
=> W+C= 50(equation 2).

Substitution of W+C = 50 in equation 1 gives, H+W+C= 90,
=> H+50= 90 (since W+C= 50).
=> H= 40 years.

3 years ago, the average age of H+W+C was 27.
The present average age of H+W+C /3 = 30 (each age increment by 3 so 3+3+3/3 =3)

5 years ago, the average age of w+c/2 = 20.
present average age will be w+c/2 = 25.

The present age of the husband will be h+w+c - (w+c) = 90 - 50 = 40.

Husband + Wife + Child = 27 (years) + 3 (years ago) => 30 x 3 (Members) => 90 years.
And;
Wife + Child = 20 (years) + 5 (years ago) => 25 x 2 (Members) => 50 years.

So,
Husband of present age = ( 90-50 )years.
= 40 years.

{(H+W+C)/3} -3 = 27 [(-3) is for 3 years ago].
(H+W+C)/3=30.
H+W+C=90 ---> eqn (1)

{(W+C)/2} -5 = 20 [(-5)is for 5 years ago]
(W+C)/2= 25.
W+C=50 ------> eq(2)

Substitute eq(2) in eq(1),
H+50 =90
so, H = 40 years.

H + W + C = 27 + 3 = 30(3 years),
H + W + C = 30 * 3 = 90 (3 persons),
W + C = 20 + 5 =25(5 years),
W + C = 25 * 2 = 50(2 persons),
H + W + C - W + C = H.
90 - 50 = 40years.

Sum of the present ages of H,W and C = 27 + 3 = 30 So, 30 * 3 = 90Years.
Sum of the present ages of H,W and C = 20 + 5 = 25 So, 25 * 2 = 50Years.
Hence,
Husband of presents age = (90-50)years.
= 40Years.

Wonderful explanation, thanks @Ramya.