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# [Smart Math] Ratio Proportion Problem 59

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

### Problem

R can do a piece of work in 20 days and K in 25 days. They work together for 5 days and then K leaves. In how many days would R finish the work?

1. 5
2. 9
3. 10
4. 11
5. 12

### The Usual Method

R can finish $\frac{1}{20}$ of the work in 1 day.

K can finish $\frac{1}{25}$ of the work in 1 day.

Thus total work finished by R and K working together for 5 days = $\frac{5}{20}+\frac{5}{25}=\frac{25+20}{100}=\frac{45}{100}$.

Hence remaining work = $1-\frac{45}{100}=\frac{55}{100}$.

Since R has to work alone now and R can finish $\frac{1}{20}$ of the work in 1 day, so for R to finish $\frac{55}{100}$ of the work, it will take,

1                      $\frac{1}{20}$

x $\frac{55}{100}$

By cross multiplication, we get:

$\frac{55}{100}\times \frac{20}{1}=$ 11 days more.

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

R will finish $\frac{5}{20}$ or 25% of the work in 5 days. K will finish $\frac{5}{25}$ or 20% of the work in 5 days. So, work remaining to be done = 100% – (25% + 20%) = 55%.