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Percentages Smart Math

[Smart Math] Percentages Problem 7

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

Percentages

Problem

B earns 20% more than A, C earns 25% more than B and D earns 30 % more than C. If D earns $975, what does A earn?

  1. $195
  2. $375
  3. $450
  4. $500
  5. $600

The Usual Method

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Let the earning of A be ‘1’

Hence,

B will earn 1.20a

C will earn 1.25 x 1.20a

D will earn 1.30 x 1.25 x 1.20a

Since D’s earning = $975

1.30 x 1.25 x 1.20a = 975

\therefore a=\frac{975}{1.30\times 1.25\times 1.20} = 500

(Ans: 4)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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If A’s earnings = $100

B will earn = $120 (20% more than A)

C will earn = $150 (25% more than B)

D will earn \approx $200 (30% more than C)

Since, the ratio of A’s earning to that of D is almost 1 : 2, A’s earning will be very close to half of D’s earning.

Thus approximate earning of A = 975 / 2 = 487.5.

The only answer closest to this is option’4’ = $500

(Ans: 4)

Estimated Time to arrive at the answer = 15 seconds.
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