Question 103

Amir shared 775 gifts among 4 kids. The share of the first kid, twice the share of second kid, thrice the share of third kid and four times the share of fourth kid are all equal. Find the sum of gifts received by 1st kid and 2nd kid.

Solution

Let share of each kid be $$a,b,c,d$$ respectively.

Then according to ques, => $$a=2b=3c=4d=k$$

=> $$a=k$$ , $$b=\frac{k}{2}$$ , $$c=\frac{k}{3}$$ , $$d=\frac{k}{4}$$

Thus, total = $$a+b+c+d=500$$

=> $$k+\frac{k}{2}+\frac{k}{3}+\frac{k}{4}=775$$

=> $$k\times(\frac{12+6+4+3}{12})=775$$

=> $$k=775\times\frac{12}{25}=372$$

$$\therefore$$ Sum of gifts received by 1st kid and 2nd kid = $$a+b=k+\frac{k}{2}=3\frac{k}{2}$$

= $$3\times\frac{372}{2}=558$$

=> Ans - (A)