121.A and B can do a piece of work in 10 days. If A works for 2.5 days and B works for 8.5 days then they can complete half of the work. Find the time taken by B to complete the work alone.

A और B एक कार्य को 10 दिन में पूरा कर सकते हैं। यदि A, 2.5 दिन के लिए कार्य करता है तथा B, 8.5 दिन के लिए कार्य करता है, तो वे कार्य का आधा भाग पूरा कर सकते हैं, तो B अकेले इस कार्य को कितने दिनों में पूरा करेगा?


Option”D” is correct

A and B can do a piece of work in 10 days,

⇒ Total work = (a + b) × 10

where a is A’s one day work and b is B’s one day work

If A works for 2.5 days and B works for 8.5 days, then they can complete half of the work.

To complete the full work, A will work for 5 days and B will work for 17 days,

⇒ Total work = (a × 5 + b × 17)

⇒ (a + b) × 10 = (a × 5 + b × 17),

⇒ a/b = 7/5

⇒ Total work = (a + b) × 10 = 120

∴ B will do the work in 120/5 = 24 days

122. A and B can complete a task in 1.5 days. However, A had to leave a few days before the task was completed and hence it took 2 days in all to complete the task. If A alone could complete the work in 2.625 days, how many days before the work getting over did A leave?

A और B एक काम को 1.5 दिन में पूरा कर सकते हैं। हालाँकि, काम पूरा होने से कुछ दिन पहले A को काम छोड़ना पड़ा और इसलिए काम पूरा करने में कुल 2 दिन का समय लगा। यदि A अकेले काम को 2.625 दिनों में पूरा कर सकते है, तब ज्ञात कीजिए कि काम पूरा होने से कितने दिन पहले A काम छोड़ देता है?


Option”D” is correct

⇒ A’s efficiency = 1/A = 1/2.625

⇒ (A + B)’s efficiency = (1/A) + (1/B) = (1/1.5)

⇒ (1/B) = (1/1.5) – (1/2.625) = 750/2625 = 10/35 = 2/7

Let A work for x days

⇒ Work done by A + Work done by B =1

⇒ (x/2.625) + {(2 × 2)/7} = 1

⇒ (8x/21) + (4/7) = 1

⇒ 8x/21 = 3/7

⇒ x = 9/8 = 1.125

⇒ A left the work for = 2 – x = 2 – 1.125 = 0.875

123. 4 boys from school A and 6 boys from school B together can set up an exhibition in 5 days, which 5 boys from school A and 10 boys from school C together can do in 4 days or 3 boys from school B and 4 boys from school C together can do in 10 days. Then how many boys from school A can set up the exhibition in one day?

विद्यालय A से 4 लड़के और विद्यालय B से 6 लड़के 5 दिनों में एक प्रदर्शनी लगा सकते हैं, जिसे विद्यालय A के 5 लड़के और विद्यालय C के 10 लड़के 4 दिनों में या विद्यालय B के 3 लड़के और विद्यालय C के 4 लड़के 10 दिनों में लगा सकते हैं। तो विद्यालय A के कितने छात्र एक दिन में प्रदर्शनी लगा सकते हैं?


Option”C” is correct

As we know,

Total work of first group = total work of second group = total work of third group

(4A + 6B) × 5 = (5A + 10C) × 4 = (3B + 4C) × 10

(4A + 6B) × 5 = (3B + 4C) × 10

4A + 6B = 6B + 8C

4A = 8C

A : C = 8 : 4

A : C = 2 : 1     …(1)

Again,

(5A + 10C) × 4 = (3B + 4C) × 10

20A + 40C = 30B + 40C

20A = 30B

A : B = 30 : 20

A : B = 3 : 2     …(2)

From equation (1) and equation (2)

A : B : C : = 6 : 4 : 3

Total work = (4A + 6B) × 5 = (4 × 6 + 6 × 4) × 5 = 48 × 5 = 240

Let number of students from school A complete the work be x.

x × 6 = 240

x = 240/6

x = 40

124. Two teachers A and B can complete an academic work in 10 days and 15 days respectively. They started the work together, but A left after 5 days and another teacher C joined, who alone can complete the work in 60 days. In how many days the work got completed?

दो शिक्षक A और B क्रमशः 10 दिनों और 15 दिनों में एक शैक्षणिक कार्य पूरा कर सकते हैं। उन्होंने एक साथ काम शुरू किया, लेकिन 5 दिनों के बाद A ने कार्य छोड़ दिया और एक अन्य शिक्षक C शामिल हो गए, जो अकेले 60 दिनों में काम पूरा कर सकते हैं। कितने दिनों में काम पूरा हो गया?


Option”A” is correct

Let total work be 60x units (LCM of 10, 15, 60)

⇒ Efficiency of A = 6x units/day

⇒ Efficiency of B = 4x units/day

⇒ Efficiency of C = x units/day

⇒ Work done in 5 days by A & B = (6x + 4x) × 5 = 50x units

⇒ Remaining work = 60x – 50x = 10x units

This work is completed by B & C

⇒ Time taken to complete the remaining work = 10x/ (4x + x)

= 10x/5x = 2 days

⇒ Total time taken to complete the work = 5 + 2 = 7 days

125. Adil and Biren together can complete a task in 20 days. Biren and Chirag together can complete the same task in 50 days. Adil and Chirag together can complete the same task in 40 days. If the same task was to be done by them alone, what would be the ratio of time taken by Adil alone to taken by Biren?

आदिल और बिरेन मिलकर एक काम को 20 दिनों में पूरा कर सकते हैं। बिरेन और चिरांग मिलकर समान काम को 50 दिनों में पूरा कर सकते हैं। आदिल और चिरांग मिलकर समान काम को 40 दिनों में पूरा कर सकते हैं। यदि समान काम केवल उनके द्वारा किया गया था, तो केवल आदिल और बिरेन द्वारा लिए गए समय का अनुपात क्या होगा?


Option”A” is correct

Let, Adil’s efficiency = x/day

Biren’s efficiency = y/day

Chirag’s efficiency = z/day

According to the question,

⇒ x + y = 1/20     … (1)

According to the question,

⇒ y + z = 1/50    …(2)

According to the question,

⇒ x + z = 1/40     …(3)

From (1) + (2) + (3) we get,

⇒ 2(x + y + z) = 1/20 + 1/50 + 1/40 = (10 + 4 + 5)/200 = 19/200

⇒ x + y + z = 19/400    … (4)

From (4) – (2) we get,

⇒ x = 19/400 – 1/50 = (19 – 8)/400

⇒ x = 11/400

From (4) – (3) we get,

⇒ y = 19/400 – 1/40

⇒ y = (19 – 10)/200

⇒ y = 9/200

∴ Ratio of efficiency of Adil and Biren = 11/400 ∶ 9/400 = 11 ∶ 9

∴ Ratio of time taken by Adil and Biren = 1/11 ∶ 1/9 = 9 ∶ 11

126. If 12 persons working 12 hours a day dig 12 meters of a tunnel in 12 days how many men are required to dig additional 4 meter of the tunnel (of the same dimension) given that they work 4 hours a day for 4 day?

यदि 12 व्यक्ति प्रति दिन 12 घंटे काम करके 12 मीटर के एक सुरंग को 12 दिनों में खोदते हैं, तो सुरंग (समान आयाम का) का अतिरिक्त 4 मीटर खोदने के लिए कितने पुरुषों की आवश्यकता है, दिया गया है कि वे 4 दिनों के लिए एक दिन में 4 घंटे काम करते हैं?


Option”D” is correct

Let the number of men required be x

(12 × 12 × 12)/12 = (x × 4 × 4)/4

⇒ x = 36 

∴ Number of men required be 36

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