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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 25

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

Ratio Proportion

Problem

B receives 1/8th of the profit of business as wages and the rest is divided between B and A in proportion to their capitals of $6000 and $8000 respectively. If in 1 year, B receives $1000 totally, what does A receive?

  1. $800
  2. $1000
  3. $1200
  4. $1250
  5. $1500

The Usual Method

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Assuming the total profit = ‘p

Hence, 1/8th of profit = \frac{1}{8}p

Balance profit = \frac{7}{8}p

This balance profit is divided in the ratio of investments i.e. 6000 : 8000 = 3 : 4

Hence total earnings of A = \frac{4}{7}\left( \frac{7}{8}p \right)=\frac{4}{8}p=\frac{1}{2}p

Similarly, total earnings of B = \frac{1}{8}p+\frac{3}{7}\left( \frac{7}{8}p \right)=\frac{4}{8}p=\frac{1}{2}p = $1000

\therefore p = $2000

Hence, A’s share = \frac{2000}{2} = $1000

(Ans: 2)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Visualize that the total profit is divided in 8 parts, of which 1 part goes to B as wages and the remaining 7 parts are divided between B and A in the ratio of 6000 : 8000 or 3 : 4. Thus B receives 3 more parts of the profit and A receives 4 parts. Thus B receives in total 3 + 1 = 4 parts of the profit which is same as 4 parts received by A. Thus A receives the same money as B receives i.e. $1000.

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.
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