Categories

# [Smart Math] Ratio Proportion Problem 4

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

### Problem

3 men and 6 women can dig a well in 4 days. 5 men and 4 women take 3 days. How many days would 8 women and 1 man take?

1. 6 days
2. 8 days
3. 10 days
4. 4 days
5. 9 days

### The Usual Method

Let ‘m’ be the fraction be the amount of work done by 1 man in 1 day and ‘w’ be the fraction of work done by 1 woman in 1 day.

$\therefore$3m + 6w = 1/4

$\therefore$12 m + 24 w = 1                                       …… Eq. 1.

Similarly, 5m + 4w = 1/3

$\therefore$15m + 12w = 1                                         …… Eq. 2.

Solving both equation 1 and 2 simultaneously we get

18m = 1 and 72w = 1

$\therefore$m = $\frac{1}{18}$ and w = $\frac{1}{72}$

$\therefore$8w + 1m = $\frac{8}{72} + \frac{1}{18} = \frac{3}{18} = \frac{1}{6}$

Hence, 6 days.

(Ans: 1)

Estimated Time to arrive at the answer = 120 seconds.