21. Efficiency of A is twice the efficiency of B. Efficiency of C is 150% of B. A works for 6 days, B works for 15 days and C works for 7 days to finish a work. If a total of Rs. 6000 was allocated to finish the work then the amount received by C was?

A की कार्यक्षमता, B के कार्यक्षमता की दोगुनी है। C की कार्यक्षमता, B के कार्यक्षमता की 150% है। एक कार्य को पूरा करने के लिए, A 6 दिन तक कार्य करता है, B 15 दिन तक कार्य करता है और C 7 दिन तक कार्य करता है। यदि कार्य पूरा करने के लिए कुल 6000 रु. आवंटित किए गए थे, तो C द्वारा प्राप्त राशि क्या थी?


Option”B” is correct

Let the efficiency of A, B, and C be A, B, and C unit per day

According to the question,

A = 2B

⇒ C = (150/100) × B

⇒ 3B = 2C

The ratio of A, B, and C = 4 : 2 : 3

The ratio of Amount of works done by A, B, and C = (4 × 6) : (2 × 15) : (3 × 7)

= 24 : 30 : 21 = 8 : 10 : 7

∴ Amount received by C = 6000 × (7/25) Rs.

= Rs. 1680

22.In a village Under Mission Kakatiya, 38 men working 6 hours a day can do a piece of work in 12 days. Find the number of days in which 57 men working 8 hours a day can do the same work. Assume that 2 men of the first group do as much work in 1 hour as 3 men of the second group do in 1(1/2) hours

मिशन काकतीय के तहत एक गांव में, दिन में 6 घंटे कार्य करने वाले 38 पुरुष 12 दिनों में एक कार्य पूरा कर सकते हैं। उन दिनों की संख्या ज्ञात कीजिये, जिसमें दिन में 8 घंटे कार्य करने वाले 57 पुरुष उस कार्य को पूरा कर सकते हैं। मान लीजिये कि पहले समूह के 2 पुरुष 1 घंटे में उतना कार्य करते हैं जितना कार्य दूसरे समूह के 3 पुरुष 1(12/2) घंटे में करते हैं।


Option”A” is correct

⇒ Total work = 38 × 9 × 6 × 12

⇒ 2nd group time = (38 × 9 × 6 × 12)/(57 × 4 × 8) = 27/2 days

⇒ 13.5 days

∴ Required time is 13.5 days

23. The ratio of efficiency of P, Q, and R is 5 : 6 : 4. If the difference between wages of P and R of 10 days is Rs. 750, then find per day wages of Q.

P, Q और R की दक्षता का अनुपात 5 : 6 : 4 है। यदि 10 दिनों की P और R की मजदूरी के बीच का अंतर 750 रुपये है, तो Q की प्रति दिन की मजदूरी ज्ञात कीजिए।


Option”D” is correct

Difference between wages of P and R of 10 days is Rs. 750

⇒ Difference between wages of P and R per day = Rs. 750/10 = Rs. 75

Ratio of efficiency of P, Q and R = 5x : 6x : 4x

⇒ Difference between wages of P and R per day = 5x – 4x = Rs. 75

⇒ x = Rs. 75

⇒ Per day wages of Q = 6x = 6 × Rs. 75 = Rs. 450

24. X and Y each working alone can build a wall in 8 days and 12 days respectively. They together accepted to build the wall for Rs. 9000. They worked together for 2 days and completed the remaining work with the help of Z in another 2 days. How much money will Z receive?

X और Y प्रत्येक अकेले क्रमशः 8 दिनों और 12 दिनों में एक दीवार का निर्माण कर सकते हैं। उन्होंने एक साथ 9000 रुपये में दीवार का निर्माण करना स्वीकार कर लिया। उन्होंने 2 दिनों तक एक साथ कार्य किया और शेष 2 दिनों में Z की मदद से शेष कार्य पूरा किया। Z को कितना पैसा मिलेगा?


Option”B” is correct

In building the wall, X and Y worked for 4 days each, while Z worked for only 2 days

Work done by X in 1 day = 1/8

Work done by Y in 1 day = 1/12

⇒ Work done by X and Y together in 4 days = 4 × (1/8 + 1/12) = 4 × 5/24 = 5/6

⇒ Work done by Z in 2 days = 1 – 5/6 = 1/6

∵ Total money paid = Rs. 9000

∴ Money received by Z = 1/6 × 9000 = Rs. 1500

25. 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. 35000. The share of B (in Rs.) in the contracted money will be:

A और B एक कार्य को क्रमश 15 दिन और 10 दिन में पूरा कर सकते है। उन्हें एक कार्य को पूरा करने के लिए 35000 रूपये का कॉन्ट्रैक्ट प्राप्त होता है। कॉन्ट्रैक्ट में दी गयी राशी में B का (रूपये में ) हिस्सा क्या है:


Option”A” is correct

Total work = LCM of the time taken by A and B.

Total work = 30

Efficiency = total work/time taken

Efficiency of A = 30/15 = 2 units/day

Efficiency of B = 30/10 = 3 units/day

The share was given in the ratio of their efficiencies = 2 : 3

(2 + 3) units = 35000

1 unit = 7000

B’s share = 3 × 7000 = 21000

26.Ranu and Shanu undertake to complete a piece of work for Rs. 1500. Ranu can do it in 6 days, Shanu can do it in 9 days and with the help of Anu they complete the work in 3 days. Find the share of Anu.

रानू और शानू 1500 रुपये में एक कार्य पूरा करने के लिए लेते है। रानू इसे 6 दिनों में कर सकता है, शानू इसे 9 दिनों में कर सकता है और अनु की मदद से वें इसे 3 दिनों में पूरा कर लेते हैं। अनु का हिस्सा ज्ञात कीजिए।


Option”A” is correct

Let, Anu can complete the job in x days

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

On solving above equation, we get

x = 18 days

Now, efficiency of Ranu, Shanu and Anu are in the ratio of 1/6 : 1/9 : 1/18 = 3 : 2 : 1

∴ Share of Anu = (1/6) × 1500 = Rs. 250

27.Wages of 33 girls for 48 days come to Rs. 25344. How many boys are needed for 36 days to receive Rs. 19440, if the daily wages of a boy being 2.25 times those of a girl?

48 दिनों के लिए 33 लड़कियों का वेतन 25344 रुपये होता है। 19440 रुपये प्राप्त करने के लिए 36 दिनों के लिए कितने लड़कों की आवश्यकता होती है, यदि एक लड़के का दैनिक वेतन लड़की से 2.25 गुना है?


Option”C” is correct

The wages of 33 girls for 48 days is Rs. 25344.

A boy’s wage is 2.25 times a girl’s.

Total wages of boys for 36 days work = Rs. 19440

Calculation:

Wages of 1 girl for 1 day = 25344/(33 × 48) = Rs. 16

So the wages of 1 boy for 1 day = 2.25 × 16 = Rs. 36

Number of boys required for 36 days = 19440/(36 × 36) = 15

∴ 15 boys are needed for 36 days to receive Rs. 19440

28. A and B can do a work in 20 days and 60 days respectively. If they work together with W for 10 days and completes the work and total amount earned for completion of work is Rs. 1200. What is the wages of W’s from the amount received?

A और B  एक कार्य को क्रमशः 20 दिनों में और 60 दिनों में कर सकता है। यदि वे W के साथ मिलकर एकसाथ 10 दिन तक कार्य करते है और उसे पूरा करते है और कार्य पूरा करने पर कुल 1200 रूपये कमाते है, तो कमाई गई राशि में से W का हिस्सा क्या होगा?


Option”A” is correct

Let the total work done be LCM of (10, 20, 60) = 60 units

⇒ A’s efficiency = 60/20 = 3

⇒ B’s efficiency = 60/60 = 1

⇒ (A + B + W)’s Efficiency = 60/10 = 6

⇒ W’s Efficiency = 6 – (3 + 1) = 2

Since, wages ∝ Efficiency (when number of working days is same.)

Ratio of A, B and W Efficiency = 3 : 1 : 2

Let the wages of A be 3x , wages of B be x and wages of W be 2x

Total wages of A, B and W = 6x

⇒ 6x = Rs. 1200

⇒ x = Rs. 200

So, the Wages of W = 2 × (200) = Rs. 400

∴ The wages of W’s from the amount received is Rs. 400.

29. Vishal, Jai, and Gopal undertook a typing job for Rs. 3080. Vishal and Jai alone can complete the job in 14 and 11 days respectively. They both worked for 4 days and the rest of the job is completed by Gopal in 6 days. What is the share of Jai?

विशाल, जय और गोपाल ने 3080 रुपये के लिए टाइपिंग का एक कार्य लिया। विशाल और जय अकेले क्रमशः 14 और 11 दिनों में कार्य को पूरा कर सकते हैं। उन दोनों ने 4 दिन के लिए कार्य किया और शेष कार्य गोपाल द्वारा 6 दिनों में पूरा किया गया। जय का हिस्सा क्या है?


Option”A” is correct

Suppose the total units of work = 154 units (LCM of 14 and 11);

∴ Efficiency of Vishal = 154/14 = 11

Efficiency of Jai = 154/11 = 14

Suppose the efficiency of Gopal = x;

Since Vishal and Jai worked for 4 days and rest of the job is done by Gopal in 6 days;

∴ (11 + 14) × 4 + 6x = 154;

⇒ x = 9

∴ Efficiency of Gopal = 9

∴ Ratio of work done by Vishal, Jai and Gopal = (11 × 4) : (14 × 4) : (9 × 6) = 22 : 28 : 27

Since the total amount for the job = Rs. 3080;

∴ Share of Jai = (28/77) × 3080 = Rs. 1120

Alternate Method

L.C.M of 14 and 11 = 154 = Total work

Efficiency of Jai = 154/11 = 14 units/day

Efficiency of Vishal = 154/14 = 11 units/day

Work done by Jai in 4 days = 14 × 4 = 56 units

Total amount = Rs. 3080

Share of Jai = (Work done by Jai/Total work) × Total amount

⇒ (56/154) × Rs. 3080

⇒ Rs. 1120

∴ Share of Jai is Rs. 1120

30. A, B and C can complete a work in 10 days. They start together and 60% of the work is done by B and C. A worked only for 2 days with B and C and then left. B takes 20% less time than C. If Rs. 3000 is paid for whole work then find the share of B.

A, B और C एक काम को 10 दिनों में पूरा कर सकते हैं। वे एक साथ कार्य शुरू करते हैं और B और C द्वारा 60% काम किया जाता है। A ने केवल 2 दिनों के लिए B और C के साथ काम किया और फिर छोड़ दिया। B, C से 20% कम समय लेता है। यदि इस पूरे कार्य के लिए 3000 रूपये का भुगतान किया जाता है, तो B का हिस्सा ज्ञात कीजिए।


Option”A” is correct

As, B and C did 60% work,

So, A has done 40% work

⇒ Share of A = 40% of 3000 = Rs. 1200

⇒ Share of B and C = Rs. (3000 – 1200) = 1800

Now, B takes 20% less time than C,

⇒ Working efficiency of B and C are in the ratio = 5 ∶ 4 [∵ inverse of time ratio]

∴ Share of B = (5/9) × 1800 = Rs. 1000

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