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# [Smart Math] Percentages Problem 7

Here’s and example of a SMART MATH problem for 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

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 [contentblock id=google-adsense-post] 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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