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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 41

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

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

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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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