Here’s and example of a SMART MATH problem for RATIO PROPORTION.
Problem
Of an amount of $1500 divided between A, B and C, B’s share is $70 more than C’s and A’s share is $100 less than C’s. What is A’s share?
- $410
- $425
- $450
- $490
- $510
The Usual Method
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Let the shares of A, B and C be ‘1’, ‘2’ and ‘3’ respectively.
Hence, a + b + c = 1500
Also, b = c + 70
a = c – 100
Hence, a + b + c = (c – 100) + (c + 70) + c = 1500
3c – 30 = 1500
c = 510
a = 510 – 100 = 410
(Ans: 1)
Estimated Time to arrive at the answer = 45 seconds.
Using Technique
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Consider each option. Assume A’s share = 410, C’s will be = 510 as A’s share is $100 less than C’s. B’s share will be 510 + 70 = 580.
Now check 410 + 580 + 510 = 1500
This satisfies the condition that the total amount = $1500 and hence, option ‘1’ is the correct option.
(Ans: 1)
Estimated Time to arrive at the answer = 15 seconds.
(Note: Here it is purely coincidental that the first option itself is correct. However, one can mentally check all options by this method and find that it is much easier, if not time saving.)
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