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SSC GD Constable (Held On: 16 Nov 2021 Shift 1) Memory Based Paper

Option 4 : 8 minutes

**Given:**

Three taps M, N and O together can fill an empty tank = 16/7 minutes

The tap N alone can fill it = 16 minutes

The tap O alone can fill it = 4 minutes

**Formula used:**

Fill the tank by M, N and O = MNO/(MN + NO + OM)

**Calculation:**

Let the time taken by M be x hours

Fill the tank by M, N and O = (x × 16 × 4)/(16x + 64 + 4x)

⇒ 16/7 = 64x/(20x + 64)

⇒ 320x + 1024 = 448x

⇒ 128x = 1024

⇒ x = 8

∴ M alone can fill the tank in 8 minutes.

**Alternate method **

M + N + O = 16/7 [L.C.M. of 16/7, 16 and 4 is **16 **(total unites)] so efficiency of M + N + O = 16 ÷ 16/7 = 7

N = 16 efficiency of N = 16/16 = 1

O = 4 efficiency of O = 16/4 =4

⇒ Now the efficiency of M = (efficiency of M + N + O) – efficiency of N – efficiency of O

⇒ The efficiency of M = 7 – 1 – 4 = 2

⇒ M alone can fill the tank = total unites/ efficiency of M

∴ M alone can fill the tank = 16/2 = 8 minutes