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# [Smart Math] Ratio Proportion Problem 12

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

### Problem

A, B and C can together complete a piece of work in 10 days. If B does half of what A and C do in 1 day, in how many days can B alone finish the work?

1. 20 days
2. 30 days
3. 40 days
4. 50 days
5. cannot be determined

### The Usual Method

Let the amount of work that A, B and C do individually per day be ‘1’, ‘2’ and ‘3’.

Then a + b + c = the amount of work done in 1 day.

Since, it takes 10 days to finish the work, a + b + c = $\frac{1}{10}$

Also, if B does half of what A and C do in a day, $b=\frac{1}{2}(a+c)$

Or $2b=a+c$

$\therefore a+b+c=\frac{1}{10}$

$=b+2b=\frac{1}{10}$

$\therefore 3b=\frac{1}{10}$

$\therefore b=\frac{1}{30}$

Hence, B alone would take 30 days to finish the work.

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.