GMAT asks you some of the very interesting problems from arithmetic in work and time problem.

Just keep in mind that you need to always find the rate of work happening.

\(Rate \; of \; Work = \frac{Total \; Work}{Time \; Taken}\)The first thing that you have to do in this kind of problem is to find the rate of the individual players and then approach the problem.

## Sample Questions

**1. A can do a work in 30 days and B can do the same work in 40 days. If they work together, on which day will they finish the work.**

General method is to take the value of work as x and make some complex fractional equation. Generally this approach may confuse you. Let’s see another method.

Assume the value of the work to be the multiple of the LCM of all the time taken by person in the question. You need to decide on your own what multiple minimum is required.

So here we will assume the work to be a multiple of the LCM i.e. 120P. For this question, we will assume the value of P as 1. Therefore units of work will be 120.

Rate at which A works \(= \frac{120}{30} = 4\)

Rate at which B works \(= \frac{120}{40} = 3\)

If they work simultaneously, the rate will add up. Therefore per day, together they will finish 4 +3 units.

Hence the total work will be finished in \(= \frac{120}{7} = 17.1\) days or on 18th day the work will complete.

Let us complicate the problem to some extent.

**2.A, B and C can do a work in 15, 20, 45 days respectively. A and B starts the work and 5 days later C joins them to complete the work. Find the number of days taken to complete the work.**

LCM of 15, 20 and 45 is 180. Let us assume the unit of work to be done is 180.

Rate of A \(= \frac{180}{15} = 12\)

Rate of B \(= \frac{180}{20} = 9\)

Rate of C \(= \frac{180}{45} = 4\)

Rate of A and B working together is 12 + 9 = 21.They work for 5 days that means 21 x 5 = 105 unit is done.

After 5 days, all three work together. So work done per day is 12 + 9 + 4 = 25.

Number of days to finish the rest of the work is \(= \frac{180 – 105}{25} = \frac{75}{25} = 3\)

Hence the work will be done in 5+3 = 8 days

I hope these techniques will ease your pressure towards time and work problems. Try this method with other work problems. You will find it more comprehensive and sorted method. For more on GMAT Quant, Click here.

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