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A man gave 20% of his salary to his only son and only daughter. The ratio of amount given to son and daughter is 3 : 2 respectively. Twice the amount what he gave to his daughter, he invested in LIC. Out of the remaining amount he gave one-fourth to his wife. After that he was left with Rs. 16800. Find out the amount invested in LIC.

A man gave 20% of his salary to his only son and only daughter. The ratio of amount given to son and daughter is 3 : 2 respectively. Twice the amount what he gave to his daughter, he invested in LIC. Out of the remaining amount he gave one-fourth to his wife. After that he was left with Rs. 16800. Find out the amount invested in LIC. Correct Answer Rs. 5600

Let the amount be ‘x’

⇒ 0.2x given to son and daughter in the ratio 3 ∶ 2

⇒ 3y + 2y = 0.2x

⇒ 5y = 0.2x

⇒ y = 0.2x/5 = 0.04x

∴ Amount given to son = 3 × 0.04x = 0.12x

Amount given to daughter = 2 × 0.04x = 0.08x

⇒ Amount invested in LIC = 2 × 0.08x = 0.16x

Remaining amount = x – 0.2x – 0.16x = 0.64x

∴ Amount given to wife = 0.64x/4 = 0.16x

⇒ 0.64x – 0.16x = 16800

⇒ 0.48x = 16800

∴ Total Salary = 16800/0.48 = 35000

∴ Amount invested in LIC = 0.16x = 0.16 × 35000 = Rs. 5600

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