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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 24

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

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

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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

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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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