Categories

# [Smart Math] Ratio Proportion Problem 6

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

### Problem

A can do a piece of work in 12 days. A and B together do the work in 8 days. How long would B alone take to complete the work?

1. 8 days
2. 10 days
3. 15 days
4. 18 days
5. 24 days

### The Usual Method

A in one day will finish $\frac{1}{12}$th of the work.

Let B finish $\frac{1}{b}$th of the work in one day.

Hence, $\frac{1}{12}+\frac{1}{b}=\frac{1}{8}$

$\therefore 8(b+12)=12b$

$\therefore 18b+96=12b$

$\therefore 4b=96$

$\therefore b=24$ Days

(Ans: 5)

Estimated Time to arrive at the answer = 45 seconds.