A father’s age is 2 years more than 4 times the age of his son. His age is also 2 years more than 5 times the age of his daughter. The average age of the father, the son and the daughter is 20 years. What is the age of the daughter ?<\/p>\n
[amp_mcq option1=”6 years” option2=”12 years” option3=”10 years” option4=”8 years” correct=”option4″]<\/p>\n
From the first two equations, we can equate the expressions for F:
\n4S + 2 = 5D + 2
\n4S = 5D
\nS = 5D \/ 4<\/p>\n
Now substitute the expressions for F and S in terms of D into the average age equation:
\n(5D + 2) + (5D \/ 4) + D = 60<\/p>\n
Multiply the entire equation by 4 to eliminate the fraction:
\n4(5D + 2) + 5D + 4D = 240
\n20D + 8 + 5D + 4D = 240
\n(20 + 5 + 4)D + 8 = 240
\n29D + 8 = 240
\n29D = 240 – 8
\n29D = 232
\nD = 232 \/ 29
\nD = 8<\/p>\n