In a family, the age of father, mother, son and grandson are A, B, C and D respectively. Given that A – B = 3, B + C = 78, C + D = 33 and the average age of the family is 34 years, then B – C is :
[amp_mcq option1=”19″ option2=”20″ option3=”21″ option4=”22″ correct=”option4″]
Given equations:
1) A – B = 3 => A = B + 3
2) B + C = 78
3) C + D = 33
Average age = (A + B + C + D) / 4 = 34.
Total age = A + B + C + D = 34 * 4 = 136.
Substitute equation 1 into the total age equation:
(B + 3) + B + C + D = 136
2B + C + D + 3 = 136
2B + C + D = 133
From equation 2, C = 78 – B.
From equation 3, D = 33 – C.
Substitute C and D in terms of B into the total age equation:
2B + (78 – B) + (33 – C) = 133
2B + 78 – B + 33 – (78 – B) = 133
B + 111 – 78 + B = 133
2B + 33 = 133
2B = 100
B = 50
Now find C using equation 2:
B + C = 78
50 + C = 78
C = 78 – 50 = 28
The question asks for B – C:
B – C = 50 – 28 = 22.
We can find A and D to check consistency:
A = B + 3 = 50 + 3 = 53
C + D = 33 => 28 + D = 33 => D = 5
Ages are 53, 50, 28, 5. Average = (53+50+28+5)/4 = 136/4 = 34. (Consistent)