Maths : Calculation of work time and work force

Calculate work time and work force.

Question 1

English:
20 workers can complete a piece of work in 15 days. If 5 more workers are added, how many days will it take to complete the same work?

Hindi:
20 मजदूर 15 दिनों में एक काम पूरा कर सकते हैं। यदि 5 मजदूर और जोड़ दिए जाएँ, तो वही काम कितने दिनों में पूरा होगा?

Solution / Explanation

Work = Workers × Days
Total work = 20 × 15 = 300 worker-days

New number of workers = 20 + 5 = 25

Required days = 300 ÷ 25 = 12 days

Answer:
👉 12 days

उत्तर:
👉 12 दिन

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Question 2

English:
A group of 12 workers can finish a job in 18 days. If the work must be completed in 12 days, how many additional workers are required?

Hindi:
12 मजदूर एक काम 18 दिनों में पूरा करते हैं। यदि काम 12 दिनों में पूरा करना हो, तो कितने अतिरिक्त मजदूर चाहिए?

Solution / Explanation

Total work = 12 × 18 = 216 worker-days

Workers needed for 12 days = 216 ÷ 12 = 18 workers

Additional workers = 18 − 12 = 6

Answer:
👉 6 additional workers

उत्तर:
👉 6 अतिरिक्त मजदूर

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Question 3

English:
25 workers can build a wall in 24 days. If 5 workers leave after 8 days, how many more days are needed to finish the remaining work?

Hindi:
25 मजदूर 24 दिनों में एक दीवार बना सकते हैं। यदि 8 दिनों बाद 5 मजदूर काम छोड़ दें, तो शेष काम कितने दिनों में पूरा होगा?

Solution / Explanation

Total work = 25 × 24 = 600 worker-days

Work done in 8 days = 25 × 8 = 200

Remaining work = 600 − 200 = 400

Remaining workers = 25 − 5 = 20

Days needed = 400 ÷ 20 = 20 days

Answer:
👉 20 more days

उत्तर:
👉 20 और दिन

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Question 4

English:
30 workers can complete an order in 20 days. If the number of workers is reduced by 10, how long will it take to complete the order?

Hindi:
30 मजदूर 20 दिनों में एक ऑर्डर पूरा कर सकते हैं। यदि 10 मजदूर कम कर दिए जाएँ, तो काम कितने दिनों में पूरा होगा?

Solution / Explanation

Total work = 30 × 20 = 600

Remaining workers = 20

Days required = 600 ÷ 20 = 30 days

Answer:
👉 30 days

उत्तर:
👉 30 दिन

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Question 5

English:
8 men can dig a trench in 10 days. How many days will 12 men take to dig the same trench?

Hindi:
8 आदमी 10 दिनों में एक खाई खोद सकते हैं। 12 आदमी वही खाई कितने दिनों में खोदेंगे?

Solution / Explanation

Total work = 8 × 10 = 80

Days required = 80 ÷ 12 = 6⅔ days

Answer:
👉 6⅔ days

उत्तर:
👉 6⅔ दिन

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Question 6

English:
40 workers can complete a project in 25 days. After 5 days, 10 more workers are added. How many more days will it take to finish the project?

Hindi:
40 मजदूर 25 दिनों में एक प्रोजेक्ट पूरा कर सकते हैं। 5 दिनों बाद 10 मजदूर और जोड़ दिए जाते हैं। शेष काम कितने दिनों में पूरा होगा?

Solution / Explanation

Total work = 40 × 25 = 1000

Work done in 5 days = 40 × 5 = 200

Remaining work = 800

New workers = 50

Days needed = 800 ÷ 50 = 16 days

Answer:
👉 16 more days

उत्तर:
👉 16 और दिन

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Question 7

English:
A job can be completed by 15 workers in 16 days. If only 10 workers are available, how many days will the job take?

Hindi:
15 मजदूर एक काम 16 दिनों में पूरा करते हैं। यदि केवल 10 मजदूर उपलब्ध हों, तो काम कितने दिनों में पूरा होगा?

Solution / Explanation

Total work = 15 × 16 = 240

Days required = 240 ÷ 10 = 24 days

Answer:
👉 24 days

उत्तर:
👉 24 दिन

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Question 8

English:
18 workers can manufacture goods in 14 days. If the work must be completed in 7 days, how many workers are needed?

Hindi:
18 मजदूर 14 दिनों में कुछ सामान बना सकते हैं। यदि काम 7 दिनों में पूरा करना हो, तो कितने मजदूर चाहिए?

Solution / Explanation

Total work = 18 × 14 = 252

Workers needed = 252 ÷ 7 = 36 workers

Answer:
👉 36 workers

उत्तर:
👉 36 मजदूर

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Question 9

English:
50 workers can complete a road repair in 30 days. After 10 days, 20 workers are removed. How many more days are required to complete the work?

Hindi:
50 मजदूर 30 दिनों में सड़क मरम्मत का काम पूरा कर सकते हैं। 10 दिनों बाद 20 मजदूर हटा दिए जाते हैं। शेष काम कितने दिनों में पूरा होगा?

Solution / Explanation

Total work = 50 × 30 = 1500

Work done in 10 days = 50 × 10 = 500

Remaining work = 1000

Remaining workers = 30

Days required = 1000 ÷ 30 = 33⅓ days

Answer:
👉 33⅓ days

उत्तर:
👉 33⅓ दिन

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Question 10

English:
6 workers can paint a building in 12 days. If the number of workers is doubled, how many days will be saved?

Hindi:
6 मजदूर 12 दिनों में एक इमारत रंग सकते हैं। यदि मजदूरों की संख्या दोगुनी कर दी जाए, तो कितने दिन बचेंगे?

Solution / Explanation

Total work = 6 × 12 = 72

New workers = 12

Days needed = 72 ÷ 12 = 6 days

Days saved = 12 − 6 = 6 days

Answer:
👉 6 days saved

उत्तर:
👉 6 दिन बचेंगे