**Tap X can fill a tank in 4 minutes. Tap Y can fill a similar tank in 6 minutes.a) What fraction of the tank is filled when Tap X is turned on after 1½ minutes?b) What fraction of the tank is filled after one minute when both taps are turned on at the same time?c) How long will it take to fill up this tank when both taps are turned on at the same time?**

**Solution**

**Q(a)**

Full Tank (Tap X) ----- 4 min

In 1½ min, it can fill up ----- 1½ min divided by 4 min = 3/8

**Answer: It can fill up 3/8 of the tank in 1½ min.**

**Q(b)**

(Tap X) 4 min ----- 1 tank

1 min ----- 1 divided by 4 = ¼ tank

(Tap Y) 6 min ----- 1 tank

1 min ----- 1 divided by 6 = 1/6 tank

Both taps on at the same time

1/4 + 1/6 = 5/12

**Answer: 5/12 of the tank will be filled if both taps are turned on at the same time after 1 min.**

**Q(c)**

Tap X takes 4 min to fill up whole tank.

Tap Y takes 6 min to fill up whole tank.

If both taps are turned on at the same time, the ratio of the volume that would be filled by Tap X to the volume filled up by Tap Y would be

(Tap X) Full tank ----- 4 min

3/5 filled ----- 3/5 x 4 min = 2.4 min

(The other 2/5 is filled by Tap Y, hence after 2.4 min, the tank would be full)

**Answer: It takes 2.4 min or 2 min 24 sec for the tank to be full if both taps are turned on at the same time.**

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