In a family, the age of father, mother, son and grandson are A, B, C and D respectively. Given that A \u2013 B = 3, B + C = 78, C + D = 33 and the average age of the family is 34 years, then B \u2013 C is :<\/p>\n
[amp_mcq option1=”19″ option2=”20″ option3=”21″ option4=”22″ correct=”option4″]<\/p>\n
Substitute equation 1 into the total age equation:
\n(B + 3) + B + C + D = 136
\n2B + C + D + 3 = 136
\n2B + C + D = 133<\/p>\n
From equation 2, C = 78 – B.
\nFrom equation 3, D = 33 – C.<\/p>\n
Substitute C and D in terms of B into the total age equation:
\n2B + (78 – B) + (33 – C) = 133
\n2B + 78 – B + 33 – (78 – B) = 133
\nB + 111 – 78 + B = 133
\n2B + 33 = 133
\n2B = 100
\nB = 50<\/p>\n
Now find C using equation 2:
\nB + C = 78
\n50 + C = 78
\nC = 78 – 50 = 28<\/p>\n
The question asks for B – C:
\nB – C = 50 – 28 = 22.<\/p>\n