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Percentages Smart Math

[Smart Math] Percentages Problem 8

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

Percentages

Problem

A house is sold by A to B at a profit of 10% and by B to C at a loss of 10%. If C pays $980,100 for it, what was the cost of the house for A?

  1. $900,000
  2. $970,299
  3. $980,100
  4. $990,000
  5. $1,000,000

The Usual Method

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Let the cost of the house to A be $‘x’.

Hence, cost price to B = 1.1x

And cost price to C = 0.9\times 1.1x

\therefore 0.9\times 1.1x=980,100

\therefore x=\frac{980100}{0.9\times 1.1}=990,000

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Assume that the cost price to A = $100

Hence, cost price to B = $110

Hence, cost price to C = $99

Note that cost price to C < cost price to A.

Thus, 980,100 < cost price to A.

This eliminates options ‘1’, ‘2’ and ‘3’.

Also note that, if the cost to A = 100; cost to C = 99, thus if cost to A = $1,000,000; cost to C = $990,000, but actual cost to C = $980,100. Thus option ‘4’ is the answer.

(Ans: 4)

Estimated Time to arrive at the answer = 15 seconds.
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