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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 17

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

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

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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.

Using Technique

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First get the ratio of earnings of A and B by the usual method, i.e. 7 : 6.

The investment period of A is 4 months and 4 is not a factor of 7. The amount of investment has to be a factor of 7 so as to get 7 in the ratio. The only option which has a multiple of 7 is option ‘3’ $3500.

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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