1. If A works for 4 hours a day for 6 days at 80% efficiency and gets paid Rs. 19200. What should be paid to B who works for 8 hours a day for 6 days at 60% efficiency?

यदि A, 80% की दक्षता के साथ 6 दिन के लिए एक दिन में 4 घंटे कार्य करता है और उसे 19200 रुपये मजदूरी मिलती है। B को कितनी मजदूरी मिलनी चाहिए जो कि 60% की दक्षता के साथ 6 दिन के लिए एक दिन में 8 घंटे कार्य करता है?


Option”B” is correct

Total working hours for A = 4 × 6 × (80/100) hours

⇒ 19.2 hours

Wage per hour = Rs.(19200/19.2)

⇒ Rs. 1000 per hour

Total working hours for B = 8 × 6 × (60/100) hours

⇒ 28.8 hours

B should be paid = Rs. (1000 × 28.8)

⇒ Rs 28,800

∴ The amount which B should be paid is Rs. 28,800

2. The ratio of the efficiencies of P, Q and R is 2 : 3 : 5. The total wages of P, Q and R for working for 14, 24 and 20 days respectively are Rs. 6000. Find the total wages of the three, when P working for 9 days, Q for 14 days and R for 8 days.

P, Q और R की दक्षताओं का अनुपात 2 : 3 : 5 है। क्रमशः 14, 24 और 20 दिन काम करने के लिए P, Q और R का कुल वेतन ₹ 6000 है। P के 9 दिन, Q के 14 दिन और R के 8 दिन काम करने पर तीनों का कुल वेतन ज्ञात कीजिये।


Option”A” is correct

Ratio of the work done by P, Q and R = (2 × 14) : (3 × 24) : (5 × 20) = 7 : 18 : 25

Total wage of P = {7/50} × 6000 = 840

∴ Daily wages of P = 840/14 = 60

Similarly,

Daily wages of Q = (18/50) × (1/24) × 6000 = 90

Daily wages of R = (25/50) × (1/20) × × 6000 = 150

∴ Total wages of P, Q and R working for the given periods = (60 × 9) + (90 × 14) + (150 × 8) = 3000

3. Rs. 10,000/- has to be distributed among 3 craftsmen, 5 helpers and 6 laborer’s such that each helper receives the amount twice as much as a laborer receives and each craftsman received the amount thrice as much as a laborer receives. What is the amount received by the three craftsman?

3 शिल्पकारों, 5 सहायकों और 6 मजदूरों के बीच 10,000/- रु. वितरित किया जाना है, ताकि प्रत्येक सहायक को एक मजदूर को मिलने वाली राशि से दो गुनी राशि प्राप्त हो और प्रत्येक शिल्पकार को एक मजदूर को मिलने वाली राशि से तीन गुनी राशि प्राप्त हो। तीनों शिल्पकार द्वारा प्राप्त राशि क्या है?


Option”D” is correct

Ratio of the amount of helper to laborer = 2 × 5 : 1 × 6 = 5 : 3

Ratio of the amount of craftsman to laborer = 3 × 3 : 1 × 6 = 3 : 2

Ratio of the amount of helper, laborer and craftsman = 10 : 6 : 9

Amount received by craftsman = 10000 × 9/25 = Rs. 3600

4.A earns Rs. 100 per hour and works for 8 hours per day. B earns Rs. 120 per hour and works for 6 hours per day. The ratio of per day wages of B to that of A is:

A प्रति घंटे 100 रुपये कमाता है और प्रति दिन 8 घंटे काम करता है। B प्रति घंटे 120 रुपये कमाता है और प्रति दिन 6 घंटे काम करता है। B और A की प्रति दिन की मजदूरी का अनुपात है:


Option”B” is correct

B earns per day = 120 × 6

A earns per day = 100 × 8

Required ratio = 120 × 6 : 100 × 8 = 9 : 10

5. A and B can complete a piece of work in 15 days and 10 days respectively. They got a contract to complete the work for Rs. 75000. The share of A (in Rs.) in the contracted money will be:

A और B किमी काम को क्रमशः 15 दिनों और 10 दिनों में पूरा करते हैं। वे एक काम को 75000 रुपये में करने के लिए संविदा लेते हैं। संविदा धनराशि में A का हिस्सा (रुपये में) क्या होगा?


Option”C” is correct

Ratio of number of days taken by A and B to complete the work = 15 : 10 = 3 : 2

∴ Ratio of efficiency of A and B = 2 : 3

Let their share is in the ratio of 2x and 3x

Now

2x + 3x = 75000

⇒ 5x = 75000

⇒ x = 15000

∴ Share of A = 2x = 15000 × 2 = Rs. 30000

6. X, Y and Z took a work for Rs. 46000. X alone takes 25% more time than Y alone to complete the work and Y alone takes 50% less time than Z alone to complete the work. Find the difference between the total wages of X and Z together and the wages of Y.

X, Y और Z ने 46000 रुपये में एक कार्य लिया। X अकेले कार्य को पूरा करने के लिए Y की तुलना में 25% अधिक समय लेता है और अकेले Y को Z की तुलना में 50% कम समय लगता है। X और Z की एकसाथ कुल मजदूरी और Y की मजदूरी के बीच का अंतर ज्ञात कीजिए।


Option”A” is correct

Let the time taken by Z alone to complete the work be a.

So, the time taken by Y alone to complete the work = a × 50/100 = a/2

And the time taken by X alone to complete the work = (a/2) × (125/100) = (5a/8)

The ratio of time taken by X alone, Y alone and Z alone to complete the work

(5a/8) : (a/2) : a = 5 : 4 : 8

Suppose the total work = LCM of 5, 4 and 8 = 40

So, the ratio of the efficiency of X, Y and Z = (40/5) : (40/4) : (40/8) = 8 : 10 : 5

Let the wages of X, Y and Z are 8b, 10b and 5b respectively.

So, 8b + 10b + 5b = 46000

b = 2000

Required difference = [(8 + 5) – 10] × 2000 = Rs. 6000

7.A and B together can complete a work in (20/3) days, B and C together can complete the same work in (50/7) days and A and C together can complete the same work in (100/9) days. If the difference between the wages of B and C is Rs. 900, then find the total wages of A, B, and C.

A और B एकसाथ एक काम को (20/3) दिनों में पूरा कर सकते हैं, B और C एकसाथ समान काम को (50/7) दिनों में और A और C एकसाथ समान काम को (100/9) दिनों में पूरा कर सकते हैं। यदि B और C के वेतनों का अंतर 900 रुपये है, तो A, B और C का कुल वेतन ज्ञात कीजिये।


Option”C” is correct

According to the question

(1/A) + (1/B) = 3/20   —- (1)

(1/B) + (1/C) = 7/50   —- (2)

(1/C) + (1/A) = 9/100   —- (3)

By adding all the three equations, we get 

(2/A) + (2/B) + (2/C) = (3/20) + (7/50) + (9/100) = 38/100

⇒ (1/A) + (1/B) + (1/C) = 19/100   —- (4)

By equation (4) – equation (1):

⇒ (1/C) = (19/100) – (3/20) = 1/25

By equation (4) – equation (2):

⇒ (1/A) = (19/100) – (7/50) = 1/20

By equation (4) – equation (3):

⇒ (1/B) = (19/100) – (9/100) = 1/10

The time taken by A, B and C alone to complete the work is 20 days, 10 days and 25 days respectively.

Suppose the total work = LCM of 20, 10 and 25 = 100 units

So, The ratio of the efficiencies of A, B and C = (100/20) : (100/10) : (100/25)

⇒ 5 : 10 : 4

Given, The difference between the wages of B and C = Rs. 900

∴ the total wages of A, B and C = 900 × 19/(10 – 4) = Rs. 2850

Alternate Method 

Let the total work be = 100 unit

(A + B)’s 1 day work = 100/20/3 = 15 unit

(B + C)’s 1 day work = 100/50/7 = 14 unit

(C + A)’s 1 day work = 100/100/9 = 9 unit

(A + B + C)’s 1 day work = 38/2 = 19 unit

Now we can find individual efficiency using above values:

Efficiency of A = 5 unit/day

Efficiency of B = 10 unit/day

Efficiency of C = 4 unit/day

Given, the difference between the wages of B and C = Rs. 900

∴ The total wages of A, B and C = 900 × 19/(10 – 4) = Rs. 2850

8. A and B undertake to complete a piece of work for Rupees 300. A can do it in 6 hours, B can do it in 9 hours and with the help of C they complete the work in 3 hours. Find the share of C?

A और B 300 रु. में एक कार्य को पूरा करने का ठेका लेते हैं। A उसे 6 घंटे में पूरा कर सकता है, B उसे 9 घंटे में पूरा कर सकता है और C की मदद से वे कार्य को 3 घंटे में पूरा कर लेते हैं। C का हिस्सा ज्ञात कीजिये।


Option”A” is correct

A can do 1/6 part of the work in 1 hour and B can do 1/9 part in 1 hour

Let C can complete the job in x hours

⇒ In 1 hour C can do 1/x part of the work

Accordingly,

1/6 + 1/9 + 1/x = 1/3

⇒ 1/x = 1/3 – 1/6 – 1/9

⇒ 1/x = (6 – 3 – 2)/18

⇒ 1/x = 1/18

⇒ x = 18 hours

Now the efficiency of A, B and C are in the ratio of 1/6 : 1/9 : 1/18

⇒ A : B : C = 3 : 2 : 1

So, share of C = 300/6 = Rs. 50

∴ The share of C is Rs. 50

9. A, B, and C together work for 3 days and earned Rs. 2034 while A and C works for 2 days and earned Rs. 850. B and C together work for 5 days and earned Rs. 2350. What is the daily income of C?

A, B और C ने एक साथ 3 दिन तक कार्य किया और 2034 रु. अर्जित किये, जबकि A और C ने एक साथ 2 दिन तक कार्य किया और 850 रु. अर्जित किये। B और C ने एक साथ 5 दिन तक कार्य किया और 2350 रु. अर्जित किये। C की दैनिक आय कितनी है?


Option”B” is correct

Total income of A, B and C is = 2034/3 = Rs. 678 Per day

Total income of A and C = 850/2 = Rs. 425 Per day

⇒ Per day income of B = (678 – 425) Rs. = Rs. 253

Total income of B and C together = 2350/5 = Rs. 470 Per day

∴ Per day income of C = 470 – 253 = Rs. 217

10. A can do a work in 6 days and with the help of B he can do same work in 4 days. If total wags earned by both are Rs. 370.20 then find the share of B.

A एक काम को 6 दिनों में पूरा कर सकता है और B की मदद से वह इसे 4 दिनों में पूरा कर सकता है। यदि दोनों के द्वारा अर्जित कुल वेतन 370.20 रुपये है, तो B का हिस्सा ज्ञात कीजिये।


Option”A” is correct

A = 6 days

⇒ Work done by A for one day = 1/6 work

⇒ A + B = 4 days

⇒ Work done by A + B for one day = 1/4 work

⇒ Work done by B for one day = 1/4 – 1/6 = 1/12 work

⇒ Ratio of their work is 1/6 : 1/12 = 2 : 1

Since wages ∝ work so Wages of A : wages of B = 2 : 1

Let the ratio be x then wages of A = 2x and wages of B = x

Given 2x + x = 370.20

⇒ 3x = 370.20

⇒ x = 123.40

∴ The share of B = x = Rs. 123.40

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