IAS 2015 — CSAT Maths

Correct Option (b)

To determine the time taken by both pipes working simultaneously, their individual filling rates are combined.

• Pipe A fills $\frac{1}{20}$201​ of the tank in 1 minute.
• Pipe B fills $\frac{1}{30}$301​ of the tank in 1 minute.
• When both pipes are opened, their combined filling rate per minute is the sum of their individual rates:

Combined rate = $\frac{1}{20} + \frac{1}{30}$201​+301​

To sum these fractions, a common denominator (LCM of 20 and 30, which is 60) is used:

Combined rate = $\frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12}$603​+602​=605​=121​ of the tank per minute.

Therefore, if both pipes fill $\frac{1}{12}$121​ of the tank in 1 minute, they will fill the entire tank in 12 minutes.

Incorrect Options:

• Option 1 (10 minutes): This would imply a combined filling rate of $\frac{1}{10}$101​ of the tank per minute. However, the calculated combined rate is $\frac{1}{12}$121​. A time of 10 minutes is faster than the actual combined rate and does not result from the correct summation of individual rates.

• Option 3 (15 minutes): This value is incorrect because it does not correspond to the sum of the individual filling rates. If the combined time were 15 minutes, the rate would be $\frac{1}{15}$151​, which is not equal to $\frac{1}{20} + \frac{1}{30}$201​+301​.

• Option 4 (25 minutes): This represents the simple average of the individual times (20 + 30) / 2 = 25 minutes. In 'work and time' problems, the combined time taken by multiple entities working together is always less than the time taken by the fastest individual entity. Since Pipe A takes 20 minutes, the combined time must be less than 20 minutes. Therefore, 25 minutes is logically incorrect.