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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 53

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

Ratio Proportion

Problem

Three men or six women do a piece of work in 20 days. In how many days can 12 men and 8 women do the same piece of work?

  1. 1\frac{3}{4}days
  2. 2\frac{1}{2}days
  3. 3\frac{3}{4}days
  4. 4\frac{1}{4}days
  5. 5\frac{1}{2}days

The Usual Method

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3 men = 6 women

\therefore 1 man = 2 women

Hence 12 men = 24 women

Hence 12 men and 8 women = 24 women and 8 women = 32 women.

If 6 women take 20 days, 32 women would take \frac{6\times 20}{32}days

= \frac{120}{32}=3\frac{3}{4}days.

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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We know that 3 men take 20 days, so 6 men would take 10 days (1/2 of 20 days), so 9 men would take 1/3 of 20 days i.e \frac{20}{3}days and so on.

We also know that 8 women = 4 men, hence total number of men = 12 + 4 = 16 men.

Approximation 16 to 15 men, and 15 men is same as 5 times of 3 men, so 15 men would take \frac{20}{5}=4days. Since actual number of men is more than 15, actual number of days will be slightly less than 4, so 3\frac{3}{4}days.

(Ans: 3)

Estimated Time to arrive at the answer = 10 seconds.
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