A) 37 yr and 28 yr |
B) 47 yr and 38 yr |
C) 50 yr and 41 yr |
D) 35 yr and 32 yr |
A) 37 yr and 28 yr |
Let the ages of mother, father and boys be \( \Large M, F, B_{1}, B_{2} \) respectively.
The total age of four members = \( \Large 19 \times 4 = 76 yr \).
Given, \( \Large \frac{B_{1}+B_{2}}{2} = \frac{11}{2} \)
\( \Large B_{1} + B_{2} = 11 \)
\( \Large M + F + B_{1} + B_{2} = 76 \)
\( \Large M + F = 76 - 11 \)
\( \Large M + F = 65 \)
\( \Large B_{1} + B_{2} = 11 \)
\( \Large M + F + B_{1} + B_{2} = 76 \)
\( \Large M + F = 76 - 11 \)
\( \Large M + F = 65 \) .....(i)
According to the question,
\( \Large \frac{B_{1}+B_{2}+F}{3} = \frac{B_{1}+B_{2}+M}{3} + 3 \)
\( \Large B_{1} + B_{2} + F = B_{1} + B_{2} + M + 9 \)
\( \Large F = M + 9 \)
\( \Large F - M = 9 \) ...(ii)
From Eqs. (i) and (ii), we get
F =37yr and M = 28yr