Quantitative Aptitudeमात्रात्मक योग्यता · नल और टंकी

Pipes and Cisternsनल और टंकी questions and answersप्रश्न और उत्तर

Pipes and cisterns is time and work with a twist: some pipes work against you.

Unlimitedअसीमित fresh questionsनए प्रश्न
Answersउत्तर always one tap awayहमेशा एक टैप दूर
1 subtopicउप-टॉपिक
SSC CGL ~1
TCS NQT ~1

Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।

How pipes and cisterns worksनल और टंकी को समझिए

Take the tank capacity as the LCM of the given times. Each filling pipe adds its units per hour; each emptying pipe or leak removes its units.

If the net rate is negative, the tank empties instead of filling. Read the question to see which one it asks for.

Tricks that save timeसमय बचाने वाली ट्रिक्स

All tricks →सभी ट्रिक्स →

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Mental mathsमानसिक गणितRarely taughtकम सिखाई जाने वाली✓ Checked on 841 cases✓ 841 मामलों पर जाँची गई

Work as a percentage per day

Use it when:कब इस्तेमाल करें: Two or three people (or pipes) working together, with days such as 8, 12, 16 or 20 that turn into friendly percentages.

Each person does 100/days % a day: 8 days → 12.5%, 10 → 10%, 12 → 8.33%, 20 → 5%.
Add the percentages (subtract for a leak), then days = 100 ÷ total.

Exampleउदाहरण

A: 10 days, B: 8 days. Together?

→ 10% + 12.5% = 22.5% a day → 100/22.5 = 4 4/9 days

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: It is the LCM method with the total work fixed at 100 units, so the fraction table you already know does the work.

Limits:सीमाएँ: Messy for days like 7 or 13 (14.28%, 7.69%): there the LCM method is cleaner.

Formulaसूत्र✓ Checked on 780 cases✓ 780 मामलों पर जाँची गई

Find one worker from “together” time

Use it when:कब इस्तेमाल करें: “A and B together take t days; A alone takes a days. How long does B take alone?”

B = a × t / (a − t).

Exampleउदाहरण

Together 6 days, A alone 10 days

→ B = 60/4 = 15 days

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: 1/B = 1/t − 1/a = (a − t)/(a t).

Limits:सीमाएँ: a must be greater than t (one person alone is always slower than the pair).

Solved examplesहल किए गए उदाहरण

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

Example 1उदाहरण 1 · Pipes and cisterns · Easyआसान
Pipes A and B can fill a swimming pool in 5 hours and 20 hours respectively. If both are opened together, in how many hours will the tank be full?
1. 3 hours
2. 4 hours
3. 5 hours
4. 6 hours
Answer:उत्तर: 4 hours
1. Capacity = 20 units.
2. Net rate = 4 + 1 = 5 units/h.
3. Time = 20 ÷ 5 = 4 hours.
Example 2उदाहरण 2 · Pipes and cisterns · Mediumमध्यम
Pipes A and B can fill a village water tank in 5 hours and 3 hours respectively, while pipe C can empty the full tank in 5 hours. If all three are opened together on an empty tank, how many hours will it take to fill it?
1. 2 hours
2. 3 hours
3. 4 hours
4. 6 hours
Answer:उत्तर: 3 hours
1. Capacity = 15 units.
2. Net rate = 3 + 5 − 3 = 5 units/h.
3. Time = 15 ÷ 5 = 3 hours.
Example 3उदाहरण 3 · Pipes and cisterns · Hardकठिन
Pipes A and B can fill a village water tank in 2 hours and 12 hours respectively, while pipe C can empty the full tank in 4 hours. If all three are opened together on an empty tank, how many hours will it take to fill it?
1. 2 hours
2. 3 hours
3. 4 hours
4. 5 hours
Answer:उत्तर: 3 hours
1. Capacity = 12 units.
2. Net rate = 6 + 1 − 3 = 4 units/h.
3. Time = 12 ÷ 4 = 3 hours.
Example 4उदाहरण 4 · Pipes and cisterns · Mediumमध्यम
Pipes A and B can fill a cistern in 35 hours and 28 hours respectively, while pipe C can empty the full tank in 70 hours. If all three are opened together on an empty tank, how many hours will it take to fill it?
1. 10 hours
2. 15 hours
3. 20 hours
4. 25 hours
Answer:उत्तर: 20 hours
1. Capacity = 140 units.
2. Net rate = 4 + 5 − 2 = 7 units/h.
3. Time = 140 ÷ 7 = 20 hours.
Example 5उदाहरण 5 · Pipes and cisterns · Mediumमध्यम
Pipes A and B can fill a village water tank in 2 hours and 12 hours respectively, while pipe C can empty the full tank in 3 hours. If all three are opened together on an empty tank, how many hours will it take to fill it?
1. 2 hours
2. 3 hours
3. 4 hours
4. 5 hours
Answer:उत्तर: 4 hours
1. Capacity = 12 units.
2. Net rate = 6 + 1 − 4 = 3 units/h.
3. Time = 12 ÷ 3 = 4 hours.
Example 6उदाहरण 6 · Pipes and cisterns · Mediumमध्यम
Pipes A and B can fill a village water tank in 30 hours and 12 hours respectively, while pipe C can empty the full tank in 20 hours. If all three are opened together on an empty tank, how many hours will it take to fill it?
1. 11 hours
2. 14 hours
3. 15 hours
4. 17 hours
Answer:उत्तर: 15 hours
1. Capacity = 60 units.
2. Net rate = 2 + 5 − 3 = 4 units/h.
3. Time = 60 ÷ 4 = 15 hours.

Common mistakesआम गलतियाँ

Treating a leak as a filling pipe.
Ignoring when a pipe is closed partway through.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न

How do I solve pipes and cisterns quickly?

Use the LCM capacity method and add or subtract the hourly rates.

What if a leak is discovered later?

Split the time into before and after the leak, and add the work done in each part.

Is this the same as time and work?

Yes. It uses the same rate idea with negative rates for outlets.