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# [Smart Math] Ratio Proportion Problem 41

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

### Problem

A, B and C invest $5000,$4000 and $6000 respectively in a business. B gets 25% of the profit for managing the business and the remaining profit is divided amongst A, B and C in the proportion of their investments. If B gets$100 less than A and C together, what is the profit?

1. $1500 2.$750
3. $500 4.$1000
5. $2500 ### The Usual Method [contentblock id=google-adsense-post] Ratio of investments of A, B and C = 5 : 4 : 6. Let the profit be$‘x’.

Hence profit to be divided = x – 0.25x = 0.75x

Hence share of A = $\frac{0.75x\times 5}{5+4+6}=0.25x$

Similarly, share of B = $\frac{0.75x\times 4}{5+4+6}=0.2x+0.25x=0.45x$

And share of C = $\frac{0.75x\times 6}{5+4+6}=0.3x$

Now since share of B = $100 less than A and C together, $0.45x+100=0.25x+0.3x$ $0.45x+100=0.55x$ $\therefore 0.1x=100$ $\therefore x=$$1000

(Ans: 4)

Estimated Time to arrive at the answer = 75 seconds.

### Using Technique

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Note that the ratio of investments of A, B and C is 5 : 4 : 6. Hence they will get a total of 5x + 4x + 6x = 15x.

Now observe the options. Since B initially gets 25% of the profit, the remaining 75% is to be divided amongst A, B and C. This remaining 75% of the profit should be divisible by 15. (from 15x), so that the shares of A, B and C are whole numbers.

So for option ‘4’ => 1000 = 250 (25%) + 750 (75%).

Here the 75% i.e \$750 is divisible by 15 and hence it is the answer.

(Note: We hit upon option ‘4’ straight as it is the easiest to break in 25% and 75%)

(Ans: 4)

Estimated Time to arrive at the answer = 15 seconds.
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