Question

'कवल
पाइप A एक टंकी को अकेला 4.5 घंटे भर सकता है, जबकि पाए
7
B के साथ मिलकर यह इसे 2.25 घंटे में भर सकता है। यदि कर्वे
पाइप A को आधे घंटे के लिए चालू किया जाता है जिसके बाद पाप
B को भी चालू किया जाता है, तो टंकी को भरने में कितना समय
लगेगा?
​

Answer 1

Given:

पाइप A एक टंकी को अकेला 4.5 घंटे भर सकता है, जबकि पाए B के साथ मिलकर यह इसे 2.25 घंटे में भर सकता है। यदि कर्वे पाइप A को आधे घंटे के लिए चालू किया जाता है जिसके बाद पाप B को भी चालू किया जाता है, तो टंकी को भरने में कितना समय लगेगा?

Pipe A can fill an empty cistern in 4.5 hours. Whereas along with Pipe B, it can fill it in 2.25 hours. If only Pipe A is turned on for half an hour after which Pipe B is also turned on, how long will it take in all to fill the cistern?

To find:

यदि कर्वे पाइप A को आधे घंटे के लिए चालू किया जाता है जिसके बाद पाप B को भी चालू किया जाता है, तो टंकी को भरने में कितना समय लगेगा?

Solution:

Pipe A can fill an empty cistern in 4.5 hrs

So, in 1 hr, Pipe A can fill = $\frac{1}{4.5}$

∴ In half hr, Pipe A will fill = $\frac{\frac{1}{2} }{4.5} = \frac{1}{9}$

Pipe A and B together can fill the empty cistern in 2.25 hrs

Let "x" hrs represents the time for which both A and B fill the cistern after pipe B was also turned on.

As given in the question, we can form an equation as:

[Work done by Pipe A in 1/2 hr ] + [Work done by pipe A and B in x hrs] = Total work done

$\implies \frac{1}{9} + \frac{x}{2.25} = 1$

$\implies \frac{0.25 + x}{2.25} = 1$

$\implies 0.25 + x = 2.25$

$\implies x = 2.25 - 0.25$

$\implies \bold{x = 2\:hrs}$

∴ Total time taken to completely fill the cistern is,

= 1/2 hr + 2 hrs

= 2 hrs 30 minutes . . . [∵ 1 hr = 60 minutes]

Thus, if only Pipe A is turned on for half an hour after which Pipe B is also turned on, in all it will take 2 hrs 30 minutes to fill the cistern.

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Also View:

Two pipes a and b can fill an empty cistern in 18 and 27 hours respectively. Pipe c can drain the entire cistern in 45 hours when no other pipe is in operation. Initially, when the cistern was empty pipe a and pipe c were turned on. After a few hours pipe, a was turned off and pipe b was turned on ins tantly. In all, it took 55 hours to fill the cistern. For how many hours was pipe b turned on?

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