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# [Smart Math] Ratio Proportion Problem 53

Here’s and example of a SMART MATH problem for 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

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

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 $\frac{20}{5}=4$days. 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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