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**There are 5 pumps connected to a tank, one larger pump and four smaller pumps. Each of the four smaller pumps works at half the rate of the larger pump. What is the ratio of time taken to fill the tank when all of the pumps are working together to time taken when the large pump is working alone?**

Since rate of working of small pump = ½* rate of large pump,

4 small pumps = 2 large pumps.

All 5 pumps are working=3 large pumps.

Ratio of capacities in the 2 situation = 3:1

Hence, ratio of time taken = 1:3

**Method 2:** Taking time taken by large pump as x hours,

Part filled by large tank in an hour = 1/x,

& Part filled by large tank in an hour = 1/2x

When all 5 pumps are working together, part filled = 1/x + 4*1/2x = 3/x

So, the time taken = x/3 hours.

Required ratio = x/3 : x = 1:3

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