Seven years ago, Prachi was four times as old as her daughter was at that time. Four years from now, Prachi will be two-and-a-half times as old as her daughter would then be. Find the sum of the present ages (in years) of Prachi and her daughter.
69
Given:
Seven years ago, Prachi was four times as old as her daughter was at that time.
Four years from now, Prachi will be two-and-a-half times as old as her daughter would then be.
Formula Used:
Let Prachi's present age be P years.
Let her daughter's present age be D years.
Seven years ago, Prachi's age = P − 7
Seven years ago, Daughter's age = D − 7
Given: P − 7 = 4(D − 7)
Four years from now, Prachi's age = P + 4
Four years from now, Daughter's age = D + 4
Given: P + 4 = 2.5(D + 4)
Calculation:
From the first equation:
P − 7 = 4(D − 7)
P − 7 = 4D − 28
P = 4D − 21 (Equation 1)
From the second equation:
P + 4 = 2.5(D + 4)
P + 4 = 2.5D + 10
P = 2.5D + 6 (Equation 2)
Equating Equation 1 and Equation 2:
4D − 21 = 2.5D + 6
Equating Equation 1 and Equation 2:
4D − 21 = 2.5D + 6
⇒ 4D − 2.5D = 6 + 21
⇒ 1.5D = 27
⇒ D = 18
Substitute D = 18 in Equation 1:
P = 4(18) − 21
⇒ P = 72 − 21
⇒ P = 51
Sum of the present ages of Prachi and her daughter:
P + D = 51 + 18
⇒ P + D = 69
The sum of the present ages of Prachi and her daughter is 69 years.
Similar Questions
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Important Questions from Problem on Age
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In a school, the average age of boys and girls together is 16.8 years, the average age of boys is 15.4 years, and the average age of girls is 18.2 years. The ratio of number of boys to girls in the school is:
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