91.In a fort, there was sufficient food for 200 soldiers for 31 days. After 27 days, 120 soldiers left the fort. For how many days will the rest of the food last for the remaining soldiers?

एक किले में 200 सैनिकों के लिए 31 दिनों का पर्याप्त भोजन था। 27 दिनों के बाद, 120 सैनिक किले को छोड़ देते हैं। तो शेष सैनिकों के लिए बचा हुआ भोजन कितने  दिनों तक चलेगा?


Option”B” is correct

Total food = 200 × 31

Food consumed in 27 days = 200 × 27

⇒ Remaining food = 200 × 31 – 200 × 27 = 200 × 4

If 120 soldiers left the army, then number of remaining soldiers = 200 – 120 = 80

Let food sufficient for 80 solders for x days

According to the question

80 × x = 200 × 4

⇒ x = (200 × 4)/80

∴ x = 10 days

92. A and B can do a job in 5 days, B and C can do the same job in 6 days and C and A can do the same job in 7.5 days. A, B, and C together will complete the same job in how many days? 

A और B 5 दिनों में एक कार्य कर सकते हैं, B और C वही कार्य को 6 दिनों में कर सकते हैं और C और A वही कार्य को 7.5 दिनों में कर सकते हैं। A, B और C मिलकर वही काम को कितने दिनों में पूरा करेंगे?


Option”B” is correct

Let total work be 30 units (LCM of 5, 6 and 7.5).

Now, efficiency of A + B = 30/5 = 6 unit/day      —- (1)

And, efficiency of B + C = 30/6 = 5 units/day      —- (2)

And, efficiency of A + C = 30/7.5 = 4 units/day      —- (3)

Adding 1, 2 and 3, we get

2(A + B + C) = 15 units/day

⇒ A + B + C = 15/2 = 7.5 units/day

∴ Time taken by A, B and C to complete the work = 30/7.5 = 4 days 

93. In a school 25 members in staff. They can make question papers in 28 hours. But due to some work after every 10 hours, 5 members left the work. Then in how much time work will be completed?

एक स्कूल में स्टाफ में 25 सदस्य हैं। वे 28 घंटे में प्रश्न पत्र बना सकते हैं। लेकिन हर 10 घंटे के बाद किसी काम की वजह से 5 सदस्यों ने काम छोड़ दिया। फिर कितने समय में कार्य पूरा होगा?


Option”C” is correct

Total members in staff = 25

Time is taken by all to make question paper = 28 hours

Thus the total work = 25 × 28 = 700 units

In the first 10 hours, work completed by 25 members

⇒ 25 × 10 = 250 units

After every 10 hours, 5 members left the work.

So, now total members = 25 – 5 = 20

In next 10 hours, work completed by 20 members

⇒ 10 × 20 = 200 units

Now again after every 10 hours, 5 members left the work.

Now members = 20 – 5 = 15

In next 10 hours, work completed by 15 members

⇒ 15 × 10 = 150 units

Now again after every 10 hours, 5 members left the work.

Now members = 15 – 5 = 10

In next 10 hours, work completed by 10 members

⇒ 10 × 10 = 100 units

Now total work done

⇒ 250 + 200 + 150 + 100 = 700 units

Now time taken to complete 700 units

⇒ 10 + 10 + 10 + 10 = 40 hours

∴ The total time taken by staff members to make question papers is 40 hours.

94. 10 men and 5 women can do a work in 60 days. If one man can do the work of two women, how long will 5 men and 20 women take to complete half of the work?

10 पुरुष और 5 महिलाएं 60 दिनों में एक काम कर सकते हैं। यदि एक पुरुष दो महिलाओं का काम कर सकता है, तो 5 पुरुषों और 20 महिलाओं को आधा काम पूरा करने में कितना समय लगेगा?


Option”A” is correct

10 men and 5 women can do a work in 60 days and one man can do the work of two women

Formula Used:

m1 × d1 = m2 × d2 = total work

Solution:

10 men and 5 women can do a work in 60 days

According to question:

⇒ work efficiency of 1 man = work efficiency of 2 women

⇒ total women = 10 × 2 + 5 = 25 women

⇒ total work = 25 women × 60 = 1500

so, half of the work = 750

since half of the work is to be done by 5 men and 20 women 

⇒ total women = 5 × 2 + 20 = 30 women

using the above formula, we have

⇒ 30 × d = 750

⇒ d = 25

∴ Total days = 25 days

95.Men and women work together in a factory manufacturing denim jeans. Men are 50% more efficient than women. Find out the total time required to manufacture 1200 units of jeans if women can manufacture 20 units of jeans in a day.

(Men and women working in the factory are equal in number.)

डेनिम जीन्स बनाने वाली एक फैक्ट्री में पुरुष और महिलाएं एक साथ कार्य करते हैं। पुरुष महिलाओं से 50% अधिक दक्ष हैं। यदि महिलाएं एक दिन में 20 इकाई जीन्स का निर्माण कर सकती हैं, तो 1200 इकाई जीन्स के निर्माण के लिए आवश्यक कुल समय ज्ञात कीजिए।

(कारखाने में काम करने वाले पुरुष और महिलाएं संख्या में बराबर हैं।)


Option”A” is correct

Work done by women = 20 units/day

⇒ Work done by men = 1.5 × 20

⇒ Work done by men = 30 units/ day

Now, Total work = 1200 units

⇒ Work done by both men and women = 20 + 30

⇒ 20 + 30 = 50 units/day

⇒ Time taken = 1200 / 50

∴ Time taken = 24 days

Note:

(Men and women working in the factory are equal in number.)

96. If A, B, and C can do a piece of work in 17, 34, and 27.2 days respectively. In how many days together they will do the same work?

यदि A, B, और C क्रमशः 17, 34 और 27.2 दिनों में एक काम कर सकते हैं। कितने दिनों में वे एकसाथ वही काम पूरा करेंगे?


Option”D” is correct

Part of work done by A in a day = 1/17

Part of work done by B in a day = 1/34

Part of work done by C in a day = 1/27.2 = 5/136

Together they will do 1/17 + 1/34 + 5/136 of the total work in a day

Together they will do 17/136 of the total work in a day

Together they will do 1/8 of the total work in a day

∴ Together they will do the work in 8 days

97.A can complete a task alone in 8 days, while B takes 12 days to do it by herself. Together with C it takes them 4 days to complete the work. If C and D together can complete the task in 15 days, then how many days will D need to complete the task by herself?

A अकेले किसी काम को 8 दिनों में पूरा कर सकता है, जबकि B को इस काम को पूरा करने में 12 दिन लगते हैं। दोनों को C के साथ मिलकर इस काम को पूरा करने में 4 दिन लगते हैं। यदि, केवल C और D दोनों मिलकर इस काम को 15 दिनों में पूरा कर सकते हैं, तो D को अकेले इस काम को पूरा करने में कितने दिन लगेंगे?


Option”B” is correct

A can complete a task alone in 8 days, while B takes 12 days to do it by herself. Together with C it takes them 4 days to complete the work,

Let the total work be 24 units,

⇒ 1 day work of A = 3 units

⇒ 1 day work of B = 2 units

⇒ 1 day work of (A, B and C) = 6 units

⇒ 1 day work of C = 1 units

⇒ C takes 24 days to complete the work alone.

C and D together can complete the task in 15 days,

Let the total work be 120 units,

⇒ 1 day work of C = 5 units

⇒ 1 day work of (C and D) = 8 units

⇒ 1 day work of D = 3 units

∴ D takes 40 days to complete the work alone

98. A contract is to be completed in 50days and 105 men were set to work, each working 8hr a day. After 25days, 2/5th of the work is finished. How many additional men be employed, so that the work may be completed on time, each man now working 9hr a day?

एक अनुबंध 50 दिनों में पूरा किया जाना है और 105 पुरुषों को प्रत्येक दिन 8 घंटे काम करने के लिए निर्धारित किया गया है। 25 दिनों के बाद, काम का दो पाचवां हिस्सा पूरा हो जाता है। यदि प्रत्येक पुरुष अब एक दिन में 9 घंटे काम करता है, तो काम पूरा करने के लिए कितने अतिरिक्त पुरुषों को नियुक्त किया जाना चाहिए?


Option”B” is correct

M1 = 105, T1= 8, D1= 25, W1 = (2/5)

Now, let the additional men be x

 M2 = (105 + x), T2 = 9, D2 = 25, W2 = 1 – (2/5) = 3/5

 W1 / (M1 × T1 × D1) =  W2 / (M2 × T2 × D2) 

⇒ (2/5) / (105 × 8 × 25)  = (3/5) / {(105 + x) × 9 × 25) 

⇒  {(105 + x) × 9} × 2 = (105 × 8) × 3

⇒  630 + 6x = 840

⇒ 6x = 210

⇒ x = 35

∴ additional 35 men are required.

99. 10 men can complete a job in 200 days. They started the work. After 20 days, 10 men with three times their efficiency joined them. The total time (in days) to complete the remaining job is∶

10 पुरुष एक कार्य को 200 दिनों में पूरा कर सकते हैं। वह कार्य प्रारंभ करते है। 20 दिनों के बाद, उनकी कार्यक्षमता की तीन गुना कार्यक्षमता वाले 10 पुरुष उनके साथ शामिल हो जाते हैं। तो शेष कार्कोय पूरा करने में लिया गया कुल समय (दिनों में) कितना है?


Option”A” is correct

Let the efficiency of 1 man be x.

As we know,

Total work = total work

M1 = 10x, D1 = 200 days and M2 = 10x, D2 = 20 days,

M3 = {10x + (10 × 3x)} = 40x

According to the question

M1 × D1 = (M2 × D2) + (M3 + D3)

(10x × 200) = (10x × 20) + (40x × D3)

(10x × 200) – (10x × 20) = (40x × D3)

10x × 180 = 40x × D3

D3 = (10x × 180)//40x = 45 days

100. It is given that men are twice as efficient than women in respect of doing a work. If three men and two women can complete the work in 2 days, then in how many days can a woman working alone complete the work?

यह दिया गया है कि काम करने के मामले में पुरुष महिलाओं से दोगुने दक्ष हैं। यदि तीन पुरुष और दो महिलाऐं काम को 2 दिनों में पूरा कर सकते हैं, तब एक महिला अकेले काम करते हुए काम को कितने दिनों में पूरा कर सकती है?


Option”B” is correct

1 man = 2 women

Work done by 3 men + 2 women = 2 days

Or (6 + 2) women do the work in 2 days.

Work done by 8 women in a day = ½

Work done by 1 woman in 1 day = 1/16

Hence, a woman working alone complete the work = 16 days

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