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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 35

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

Ratio Proportion

Problem

A and B have respectively $3000 and $4000 in a business. A receives $10/month out of the profit for running the business and the rest of the profit is divided in proportion of their investment. If in a year, A totally receives $390, what does B receive?

  1. $360
  2. $370
  3. $380
  4. $390
  5. $400

The Usual Method

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Let P be the profit at the end of the year.

Since A gets $10/month, at the end of the year, he receives (10 x 12) = $120.

Hence, balance profit to be distributed between A and B = P – 120 (i.e distributable profit)

A gets \frac{(P-120)}{(3000+4000)}\times 3000+(10\times 12) and

B gets \frac{(P-120)}{(3000+4000)}\times 4000

But A gets $390

\therefore \frac{(P-120)}{(3000+4000)}\times 3000+(10\times 12) = 390

\therefore \frac{(P-120)}{7}\times 3+120 = 390

\therefore P-120=\left( 390-120 \right)\frac{7}{3}

\therefore P-120=630

\therefore P=630+120=750

Hence B’s share = \frac{\text{(750 - 120)}}{\text{3000+4000}}\times 4000

=630\times \frac{4}{7}=360

(Ans: 1)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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If A receives $390 which includes $10 x 12 = $120

\therefore A’s share of distributable profit = 390 – 120 = 270

A and B should distribute the distributable profit in the ratio of their investments i.e. 3 : 4.

Now A’s share = 270, than B’s share will be \frac{270\times 4}{3} = $360 (according to the proportion)

(Ans: 1)

Estimated Time to arrive at the answer = 15 seconds.
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