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# [Smart Math] Percentages Problem 8

Here’s and example of a SMART MATH problem for 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

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 [contentblock id=google-adsense-post] 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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