Four years ago, a mother was four times as old as her daughter. Six years later, the mother will be two and a half times as old as her daughter at that time. Find the present ages of mother and her daughter.
Linear Equations
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Question

Four years ago, a mother was four times as old as her daughter. Six years later, the mother will be two and a half times as old as her daughter at that time. Find the present ages of mother and her daughter.

Linear Equations

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KnowledgeBoat · Accepted Answer

Let present ages of mother and her daughter be x and y years respectively. Given, Four years ago, a mother was four times as old as her daughter. ⇒ (x - 4) = 4(y - 4) ⇒ x - 4 = 4y - 16 ⇒ x = 4y - 16 + 4 ⇒ x = 4y - 12 .......(1) Given, Six years later, the mother will be two and a half times as old as her daughter at that time. ⇒ (x + 6) = 2.5(y + 6) ⇒ x + 6 = 2.5y + 15 ⇒ x = 2.5y + 15 - 6 ⇒ x = 2.5y + 9 ........(2) From (1) and (2), we get : ⇒ 4y - 12 = 2.5y + 9 ⇒ 4y - 2.5y = 9 + 12 ⇒ 1.5y = 21 ⇒ y = = 14. Substituting value of y in equation (1), we get : ⇒ x = 4 × 14 - 12 = 56 - 12 = 44. Hence, age of mother is 44 years and age of daughter is 14 years.

Mathematics

Four years ago, a mother was four times as old as her daughter. Six years later, the mother will be two and a half times as old as her daughter at that time. Find the present ages of mother and her daughter.

Linear Equations

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