The average age of father and elder son is 35 years, the average age of father and younger son is 32 years and the average age of the two sons is 17 years. What is the average age of the father and his two sons?
[amp_mcq option1=”30 years” option2=”27 years” option3=”28 years” option4=”29 years” correct=”option3″]
This question was previously asked in
UPSC CAPF – 2022
Given information:
1. Average age of father and elder son is 35 years: $(F + E)/2 = 35 \implies F + E = 70$.
2. Average age of father and younger son is 32 years: $(F + Y)/2 = 32 \implies F + Y = 64$.
3. Average age of the two sons is 17 years: $(E + Y)/2 = 17 \implies E + Y = 34$.
We need to find the average age of the father and his two sons, which is $(F + E + Y)/3$.
Adding the three equations:
$(F + E) + (F + Y) + (E + Y) = 70 + 64 + 34$
$2F + 2E + 2Y = 168$
$2(F + E + Y) = 168$
$F + E + Y = 168 / 2 = 84$.
The average age of the father and his two sons is $(F + E + Y)/3 = 84/3 = 28$ years.
– Solving a system of three linear equations with three variables.
– Calculating the final average.
$(F+E+Y) = 84$
Substitute $(E+Y)=34$: $F + 34 = 84 \implies F = 50$.
Substitute $F=50$ into $F+E=70$: $50 + E = 70 \implies E = 20$.
Substitute $F=50$ into $F+Y=64$: $50 + Y = 64 \implies Y = 14$.
Check with $E+Y=34$: $20 + 14 = 34$. The ages are 50, 20, and 14 years.
Average age of father and sons = $(50 + 20 + 14)/3 = 84/3 = 28$.