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# [Smart Math] Ratio Proportion Problem 17

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

### Problem

B invests $500 more than A in business, but A’s investment in the business is for 4 months, whereas B’s investment is for 3 months only. If A’s share of total profit of$520 is $40 more than B’s. How much did A contribute to business? 1.$2500
2. $3000 3.$3500
4. $4000 5.$4500

### The Usual Method

Let earning by A = a

Hence, earnings by B = 520 – a

Also, a – (520 – a) = 40

$\therefore a=\frac{560}{2}=280$

$\because$ Ratio of Earnings = Ratio of Investment

Hence, 280 : 240 or 7 : 6 = Ratio of Investment

Let the amount invested by A be $x Hence, amount invested by B =$(x + 500)

Thus, ratio of investments by A and B is $\frac{x\times 4}{\left( x+500 \right)\times 3}=\frac{7}{6}$

$\therefore \frac{x}{x+500}=\frac{21}{24}$

$\therefore 24x=21x+10500$

$\therefore x=3500$

(Ans: 3)

Estimated Time to arrive at the answer = 60 seconds.