Question

Two pipes can fill a tank in 12 minutes and 20 minutes respectively. Both
pipes are opened together and after some time the first pipe is closed
and the tank is full in totally 10 minutes. For how many minutes was first
pipe open?

a. 8 Min
b. 6 Min
c. 7 Min
d. 10 Min​

Answer 1

➥Question

• Two pipes can fill a tank in 12 minutes and 20 minutes respectively. Both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 10 minutes. For how many minutes was first pipe open?

➥Given

• Two pipes can fill the tank in 12 minutes and 20 minutes.

➥Solution

1st pipe can fill tank in one minute = $\large \frac{1}{12}$

2nd pipe fill tank in 1 minute = $\large \frac{1}{20}$

Both pipes fill in one minute

⇒ Tank filled by both pipes in a minute, 1/2 + 1/20 = 1/10

First pipe was open for (10-x minute)

⟹ $\large \frac{1}{12} \times (10 - x) + \frac{1}{20} \times 10 = 1$

⟹$\large \frac{10}{12} - \frac{x}{12} + \frac{1}{2} = 1$

⟹ $\large \frac{16}{12} - 1 = \frac{x}{12}$

⟹$\large \frac{4}{12} = \frac{x}{12}$

$\huge\purple{⟾}$ $\huge \mathrm \orange x \: \pink = \green 4$

$\large\blue{\mid{\fbox{\rm{∴\:It\:takes\:6\:mintues\:by\:first\:pipe}}\mid}}$