Four years ago, Ravi was four times as old as Kavya. Seven years from now, Ravi will be three times as old as Kavya. Find the sum of their present ages.
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 118 years.
Let Ravi's present age be R years and Kavya's present age be K years.
Four years ago,
Ravi's age = R - 4,
and Kavya's age = K - 4
At that time, Ravi was four times as old as Kavya.
⇒ R − 4 = 4(K − 4)
⇒ R − 4 = 4K − 16
⇒ R = 4K − 12 (Equation 1)
Seven years from now,
Ravi's age will be R + 7, and Kavya's age will be K + 7.
At that time, Ravi will be three times as old as Kavya.
⇒ R + 7 = 3(K + 7)
⇒ R + 7 = 3K + 21
⇒ R = 3K + 14 (Equation 2)
from Equation 1 and Equation 2:
⇒ 4K − 12 = 3K + 14
⇒ 4K − 3K = 14 + 12
⇒ K = 26
put K = 26 into Equation 1:
⇒ R = 4 × 26 − 12
⇒ R = 104 − 12 = 92
the Sum of Their Present Ages = R + K = 92 + 26 = 118 years