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.
Question:
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.
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.
Options
Answer: (1) 69
Explanation:
Let Prachi = P and daughter = D. Seven years ago: P − 7 = 4(D − 7) ⇒ P − 7 = 4D − 28 ⇒ P = 4D − 21 Four years from now: P + 4 = (5/2)(D + 4) Substitute P = 4D − 21: 4D − 21 + 4 = (5/2)(D + 4) 4D − 17 = (5/2)D + 10 Multiply by 2: 8D − 34 = 5D + 20 3D = 54 ⇒ D = 18 P = 4D − 21 = 72 − 21 = 51 Sum of present ages = P + D = 51 + 18 = 69 Final Answer: 69 (Option 1)
Explanation:
Let Prachi = P and daughter = D. Seven years ago: P − 7 = 4(D − 7) ⇒ P − 7 = 4D − 28 ⇒ P = 4D − 21 Four years from now: P + 4 = (5/2)(D + 4) Substitute P = 4D − 21: 4D − 21 + 4 = (5/2)(D + 4) 4D − 17 = (5/2)D + 10 Multiply by 2: 8D − 34 = 5D + 20 3D = 54 ⇒ D = 18 P = 4D − 21 = 72 − 21 = 51 Sum of present ages = P + D = 51 + 18 = 69 Final Answer: 69 (Option 1)
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