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# [Smart Math] Ratio Proportion Problem 24

Here’s and example of a SMART MATH problem for RATIO PROPORTION. ### Problem

$336 is to be divided between A and B such that A gets $\frac{5}{16}$th of what B gets. What amount does A get? 1.$75
2. $80 3.$100
4. $105 5.$125

### The Usual Method

Let the share of A be = ‘1’

And the share of B be = ‘2’ $\therefore a=\frac{5}{16}b$ $\therefore 16a=5b$

Hence, A’s share = $\frac{5\times 336}{\left( 5+16 \right)}=\frac{5\times 336}{21}=80$

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Since A’s share = $\frac{5}{16}$ of B, $\frac{a}{b}=\frac{5}{16}$, where ‘1’ and ‘2’ are the shares of A and B respectively.

Since all options are multiples of 5, the share of B under each option will be:

A’s share                     B’s share

75                    336 – 75 = 261 (not a multiple of 16)

80                    336 – 80 = 256 (is a multiple of 16)

No need to check further since, there can be only one answer. Hence, option ‘2’ is the answer.

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.

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