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# [Smart Math] Ratio Proportion Problem 35

Here’s and example of a SMART MATH problem for 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 [contentblock id=google-adsense-post] 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

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)