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.

Let total salary of the man be Rs. $$100x$$

Total amount given to his son and daughter = $$\frac{20}{100} * 100x = 20x$$

Amount given to daughter = $$\frac{2}{5} * 20x = 8x$$

Amount invested in LIC = $$8x * 2 = 16x = ?$$

Remaining amount = $$100x - 20x - 16x = 64x$$

Amount given to wife = $$\frac{1}{4} * 64x = 16x$$

=> Remaining amount = $$64x - 16x = 48x$$

Acc to ques : $$48x = 16800$$

=> $$x = 350$$

$$\therefore$$ Amount invested in LIC = 16 * 350 = Rs. 5600