Question

Three sons of a man have Rs.12, Rs.15 and Rs.19 with them. The father asks his sons to give him equal amount so that the money held by the sons now are in continued proportion. Find the amount taken from each son.

Answer 1

Let the amount taken from each of them is $ p.

Then, according to the problem

12 – p, 15 – p and 19 – p are in continued proportion.

Therefore,

12−p/15−p = 15−p/19−p

⟹ (12 – p)(19 – p) = (15 – p)22

⟹ 228 – 12p – 19p + p22 = 225 – 30p + p22

⟹ 228 – 31p = 225 – 30p

⟹ 228 – 225 = 31 p – 30p

⟹ 3 = p

⟹ p = 3

Therefore, the required amount is $ 3.

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Answer 2

Let the amount taken from each of them is Rupees p.

Given That :-

12 – p, 15 – p and 19 – p are in continued proportion.

Therefore,

12−p:15−p : : 15−p:19−p  

⟹ (12 – p)(19 – p) = (15 – p)(15 – p)

⟹ 228 – 12p – 19p + p^2 = 225 – 30p + p^2  

⟹ 228 – 31p = 225 – 30p

⟹ 228 – 225 = 31 p – 30p

⟹ 3 = p    (or)

⟹ p = 3

Therefore,the required amount is Rupees 3.

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