31. A and B together are supposed to do 13/15 of the work and B and C together 11/20 of the work. If the difference between wages of A and C is Rs. 7600, then the total wages of A and C is:

A और B एक साथ कार्य का 13/15 और B और C एक साथ कार्य का 11/20 भाग करने वाले हैं। यदि A और C के वेतन मध्य का अंतर 7600 रुपये है, तो A और C की कुल वेतन है:


Option”A” is correct

Let total work be 60 unit,

Work done by A and B = 13/15 × 60 = 52 unit

⇒ Work done by C = 60 – 52 = 8 unit

Work done by B and C = 11/20 × 60 = 33 unit

⇒ Work done by A = 60 – 33 = 27 unit

Work done by B = 60 – 27 – 8 = 25 unit

According to the question,

27 – 8 = 19 unit = 7600

⇒ 1 unit = 400

Total wages of A and C = (27 + 8) = 35 units = 35 × 400 = Rs. 14000

32. A can complete 3/4th of work in 15 days and B can complete 4/5th of work in 24 days. With the help of C, three complete the work in 20/3 days and earn Rs. 360. If money shared in the ratio of work done, then difference in share of C and share of A is –

A, 15 दिनों में 3 / 4 भाग काम पूरा कर सकता है और B, 24 दिनों में 4 / 5 भाग काम पूरा कर सकता है। C की मदद से, तीनों 20/3 दिनों में काम पूरा करते हैं और 360 रूपये कमाते हैं। यदि पैसे को किए गए काम के अनुपात में बांटा जाता है, तो C और A के हिस्से का अंतर है –


Option”B” is correct

A can complete the work in = 15 × 4/3 = 20 days

B can complete the work in = 24 × 5/4 = 30 days.

Work done by A in 20/3 days = 20/3 × 1/20 = 1/3

Work done by B in 20/3 days = 20/3 × 1/30 = 2/9

Work done by C in 20/3 days =

= 1 – 1/3 – 2/9

= 4/9

Ratio of work done =

= 1/3 : 2/9 : 4/9

= 3 : 2 : 4

Required difference in shares =

= 360 × 4/9 – 360 × 3/9

= Rs. 40

33. A, B and C together can complete a work in 5 days, while A alone can complete the work in 15 days and B is 25% more efficient than A. Out of the total wages of Rs. 21600, find the difference between the share of B and C.

A, B और C एकसाथ एक काम को 5 दिनों में पूरा कर सकते हैं, जबकि A अकेले काम को 15 दिनों में पूरा कर सकता है और B, A से 25% अधिक दक्ष है। 21600 रुपये के कुल वेतन में से, B और C के हिस्से के बीच अंतर ज्ञात कीजिये।


Option”D” is correct

The time taken by A alone to complete the work = 15 days

So, the time taken by B alone to complete the work = 15 × 100/125 = 12 days

Given, the time taken by A, B and C together to complete the work = 5 days

So, the time taken by C alone to complete the work = (1/5) – (1/15) – (1/12) = 3/60 = 20 days

The ratio of the time taken by A, B and C individually to complete the work = 15∶ 12∶ 20

Let the total work be the LCM of 15, 12 and 20 = 60

So, the ratio of one day’s work of A, B and C individually = (60/15) ∶ (60/12) : (60/20) = 4∶ 5∶ 3

Required difference = 21600 × (5 – 3)/12 = 21600 × 2/12 = Rs. 3600

34. A contractor takes a contract to complete a road in 60 days and employed 105 labours. After 25 days, he found that one-third of the work is completed. How many more labours he required to complete the remaining work in time?

एक ठेकेदार 60 दिनों में एक सड़क को पूरा करने का एक अनुबंध लेता है और 105 मजदूरों को नियुक्त करता है। 25 दिनों के बाद, उसने पाया कि एक तिहाई कार्य पूरा हो गया है। शेष कार्य को समय पर पूरा करने के लिए उसे और कितने मजदूरों की आवश्यकता थी?


Option”D” is correct

Let total work be 3

As we know,

⇒ [M1 × D1]/W1 = [M2 × D2]/W2

⇒ [105 × 25]/1 = [M2 × 35]/2

⇒ M2 = [105 × 25 × 2]/35

⇒ M2 = 150

Number of extra labours = 150 – 105 = 45

35. P and Q together can do a job in 7 days. P is twice as efficient as Q. In how many days can P alone do the job?

P और Q एक साथ एक कार्य को 7 दिन में पूरा कर सकते हैं। P, Q से दोगुना कार्यकुशल है। P अकेले उस कार्य को कितने दिन में पूरा कर सकता है?


Option”C” is correct

Let efficiency of Q be 1 unit/day

⇒ Efficiency of P = 2 × 1 = 2 unit/day

⇒ Total work = (2 + 1) × 7 = 21 units

∴ P alone can complete the whole work in = 21/2 = 10.5 days

36. Khushi can do 1/4th of the work in 3 days, Rashmi can do 1/2th of the work in 7 days and Deepa can do 1/8 th of the same work in 2 days. If the total amount paid for the work is ₹ 8,030. How much is Rashmi’s share in it?

ख़ुशी एक कार्य का 1/4वां भाग 3 दिन में पूरा कर सकती है, रश्मि उस कार्य का 1/2वां भाग 7 दिन में पूरा कर सकती है और दीपा उस कार्य का 1/8वां भाग 2 दिन में पूरा कर सकती है। यदि कार्य के लिए भुगतान की गई कुल राशि 8,030 रु. है, तो इसमें रश्मि का हिस्सा क्या है?


Option”A” is correct

Khushi can do 1/4 th of the work in 3 days.

∴ Khushi can do the whole work in 12 days.

Rashmi can do 1/2th of the work in 7 days

∴ Rashmi can do the whole work in 14 days.

Deepa can do 1/8 th of the same work in 2 days.

∴ Deepa can do the whole work in 16 days.

Let the total work is (L.C.M. of 12, 14 and 16), i.e., 336 units

One day work of Khushi = 336/12 = 28 units

One day work of Rashmi = 336/14 = 24 units

One day work of Deepa = 336/16 = 21 units

∴ The ratio of work done by Khushi, Rashmi and Deepa = 28 : 24 : 21

Sum of the ratio = 28 + 24 + 21 = 73

So, Rashmi’s share

(24  x  110) = ₹ 2,640

37.While working together on a task, Amit and Sumit received Rs. 600 and Rs. 400 respectively. If Amit can do the task alone in 12 days, then how much time will Sumit take to do the task alone?

एक कार्य पर एक साथ काम करते समय, अमित और सुमित को क्रमशः 600 रुपये और 400 रुपये मिलते है। यदि अमित कार्य को अकेले 12 दिन में कर सकता है, तो सुमित कार्य को अकेले कितने दिनों में कर सकता है?


Option”D” is correct

Let Sumit can do the task alone in ‘x’ days

Sumit’s 1 day work = 1/x

Amit’s 1 day work = 1/12

Now, ratio of their wages = ratio of their efficiencies

⇒ 600 ∶ 400 = (1/12) ∶ (1/x)

⇒ 3/2 = x/12

⇒ x = (12 × 3)/2 = 18

∴ Sumit will take 18 days to do the task alone

38. A, B and C are assigned to complete a work. If the ratio of time of A, B, and C is 3 : 4 : 6. Find their ratio of efficiency.
A, B और C को एक काम पूरा करने के लिए सौंपा जाता है। यदि A, B, और C द्वारा लिए गए समय का अनुपात 3: 4: 6 है, तो उनकी कार्यक्षमता का अनुपात ज्ञात कीजिए।


Option”D” is correct

As we know, efficiency is inversely proportional to time

The ratio of the efficiency of A, B, and C = 1/3 : 1/4 : 1/6 = 4 : 3 : 2

39. 18 people can do a job in 49 days. How many people can finish the same job in 21 days?
18 व्यक्ति एक काम को 49 दिनों में कर सकते हैं। तो समान काम को कितने व्यक्ति 21 दिनों में कर सकते हैं?


Option”C” is correct

M1 × D1 × W2 = M2 × D2 × W1

⇒ 18 × 49 × 1 = M2 × 21 × 1

⇒ M2 = 42

∴ 42 people can finish the same job in 21 days.

40. The ratio of the efficiencies of A, B and C is 3 : 5 : 1. Working together, they can complete a piece of work in 5 days. A and B work together for 3 days. The remaining work will be completed by C alone in?
A, B और C की दक्षताओं का अनुपात 3 : 5 : 1 है। एक साथ काम करते हुए, वे एक काम को 5 दिनों में पूरा कर सकते हैं। A और B एक साथ 3 दिन काम करते हैं। शेष काम अकेले C द्वारा कितने दिनों में पूरा किया जायेगा?


Option”B” is correct

Efficiency ratio of A, B and C = 3 : 5 : 1

Total work = (3 + 5 + 1) × 5 = 9 × 5 = 45

Work done by A and B in three days = (3 + 5) × 3 = 24

Remaining work = 45 – 24 = 21

C will complete the remaining work in = 21/1 = 21 days

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