1. A started a trading firm by investing Rs. 10 lakhs. After 4 months, B joined the business by investing Rs. 15 lakhs then 2 months after B joined C too joined them by investing Rs. 20 lakhs. 1 year after A started the business they made Rs. 6,00,000 in profit. What is C’s share of the profit (in Rs.)?

A ने 10 लाख रुपये का निवेश करके एक व्यापारिक प्रतिष्ठान शुरू किया। 4 माह बाद, B, 15 लाख रुपये का निवेश करके व्यवसाय में शामिल हो गया उसके 2 माह बाद B ने 20 लाख के निवेश के साथ C को भी शामिल करवा दिया। A के व्यवसाय शुरू करने के 1 वर्ष बाद उन्होंने 6,00,000 रुपये का लाभ अर्जित किया। लाभ में C की हिस्सेदारी (रुपये में) क्या है?

Option”A” is correct

Given :

A’s investment is 10 lakhs

B’s investment is 15 lakhs

C’s investment is 20 lakhs

A invested for whole year or 12 months

B invested for 8 months (4 months less than A)

C invested for 6 months (2 months less than B)

Concept used :

Person’s share in partnership = investment × time period of his investment

Calculations :

A’s total share = 1000000 × 12 = 12000000

B’s total share = 1500000 × 8 = 12000000

C’s total share = 2000000 × 6 = 12000000

So, share of A, B and C

A : B : C = 12000000 : 12000000 : 12000000

⇒ 1 : 1 : 1

Share of C = (1/3) of 600000

⇒ 200000 rupees

∴ share of C will be 200000 rupees

2. A sum of Rs. 7,560 is divided between A, B and C such that if their shares are diminished by Rs. 400, Rs. 300 and Rs. 260, respectively, then their shares are in the ratio 4 ∶ 2 ∶ 5. What is the original share of B?

7,560 रुपए की राशि को A, B और C के बीच इस प्रकार से बाँटा गया की यदि उनका हिस्सा क्रमशः 400 रुपए, 300 रुपए और 260 रुपए से घट जाता है तो उनके हिस्से 4 ∶ 2 ∶ 5 के अनुपात में हैं। B का वास्तविक हिस्सा क्या है?

Option”A” is correct

Given :

Sum of Rs. 7560 is divided among A,B and C

If Rs 400, 300 and 260 is taken from A,B and C respectively then the ratio is 4 ∶ 2 ∶ 5

Calculation :

Shares of A,B and C is diminished by Rs.400,Rs.300 and Rs.260 respectively

⇒ Diminished sum = Rs.7560 – (400 + 300 +260)

⇒ Rs.6600

The new ratio is 4 ∶ 2 ∶ 5

⇒ 11 units = Rs.6600

⇒ 1 unit = Rs.600

⇒ Diminished share of B = 2 × 600

⇒ Rs.1200

∵ B was diminished by Rs.300

∴ Original share of B is Rs.1500

3. Three partners shared the profit in a business in the ratio 8 : 7 : 5. They invested their capitals for 7 months, 8 months and 14 months, respectively. What was the ratio of their capitals?

तीन भागीदारों ने 8: 7: 5. के अनुपात में एक व्यवसाय में लाभ साझा किया, उन्होंने क्रमशः 7 महीने, 8 महीने और 14 महीने के लिए अपनी मूलधन का निवेश किया। उनकी मूलधन का अनुपात क्या था?

Option”B” is correct

Profit ratio of three partners = 8 : 7 : 5

Period of investment of 1st partner = 7 months

Period of investment of 2nd partner = 8 months

Period of investment of 3rd partner = 14 months

Concept used:

Person’s Profit = Investment × time period

Calculation:

Let the investment and time period be 7x : 8y : 14z

7x/8y = 8/7

⇒ 49x = 64y

⇒ y = 49x/64

7x/14z = 8/5

⇒ 35x = 112z

⇒ z = 35x/112

⇒ z = 5x/16

x : y : z = x : 49x/64 : 5x/16

⇒ Multiply by 64

x : y : z = 64 : 49 : 20

∴ The investment ratio is 64 : 49 : 20

4. A, B, C subscribe a sum of Rs. 75,500 for a business. A subscribes Rs. 3,500 more than B, and B subscribes Rs. 4,500 more than C. Out of a total profit of Rs. 45,300, how much (in Rs.) does A receive?|

A, B और C एक व्यवसाय के लिए 75,500 रु. जमा करते हैं। A, B से 3,500 रु. अधिक जमा करता है और B, C से 4,500 रु. अधिक जमा करता है, 45,300 रु. के कुल लाभ में से A को कितना प्राप्त होता है?

Option”C” is correct

Total investment = 75500

Profit = 45300

Concept used:

Person’s Profit = Investment × Time period

Calculation:

Let x be the investment of C

C = x      —-(1)

B = (x + 4500)      —-(2)

A = (x + 4500 + 3500)      —-(3)

We know that,

x + (x + 4500) + (x + 4500 + 3500) = 75500

⇒ x + (x + 4500) + (x + 8000) = 75500

⇒ 3x + 12500 = 75500

⇒ 3x = 63000

x = 21000

Put the value of x in equation 1, 2, and 3.

A = 29000

B = 25500

C = 21000

Ratio of Profit = 29000 : 25500 : 21000

⇒ 58 : 51 : 42

A’s share = [58/(58 + 51 + 42)] × 45300

∴ Share of A in the business is Rs. 17400.

5. A, B and C together invests Rs. 53,000 in a business. A invests Rs. 5,000 more than B and B invests Rs. 6,000 more than C. Out of a total profit of Rs. 31,800, find the share of A.

A, B और C मिलकर एक व्यवसाय में 53,000 रुपये का निवेश करते हैं। A, B से 5,000 रुपये और B, C से 6,000 रुपये अधिक निवेश करता है। 31,800 रुपये के कुल लाभ में से, A का हिस्सा ज्ञात कीजिए।

Option”B” is correct

Investment of A, B and C together = Rs. 53,000
Investment of A = Investment of B + Rs. 5,000
Investment of B = Investment of C + Rs. 6,000
Total profit of A, B and C together = Rs. 31800

Concept used:
If time is not given, then the investment ratio is directly proportional to the profit ratio.

Calculation:
Let the investment of C be x.
Investment of B = x + 6000
Investment of A = x + 6000 + 5000
Total investment = 53000
⇒ x + x + 6000 + x + 6000 + 5000 = 53000
⇒ 3x + 17000 = 53000
⇒ 3x = 53000 – 17000
⇒ 3x = 36000
⇒ x = 36000/3
⇒ x = 12000
Investment of A = 12000 + 11000 = 23000
Investment of B = 12000 + 6000 = 18000
Investment of C = 12000
Ratio of investment of A, B and C = 23000 : 18000 : 12000
⇒ 23 : 18 : 12
Share of A = (23/53) × 31800
⇒ 23 × 600
⇒ 13800
∴ The share of A is Rs. 13800.

6. A and B enter into a partnership with capital in the ratio 5 : 6. After 4 months, A withdraws 1/5 of his capital, while B increases his capital by 33.33%. What is the share of B(in Rs. lakhs) in the annual profit of Rs. 6.3 lakhs?

A और B, 5 : 6 के अनुपात में पूंजी के साथ साझेदारी करते हैं। 4 महीने के बाद, A अपनी पूंजी का 1/5 निकाल लेता है, जबकि B अपनी पूंजी को 33.33% में बढ़ा देता है। 6.3 लाख रूपए के वार्षिक लाभ में B (लाख रूपए में) की हिस्सेदारी क्या है?

Option”D” is correct

The ratio of A and B’s capital = 5 ∶ 6

After 4 months, A withdraws 1/5 of his capital, while B increases his capital by 33.33%

Total annual profit = Rs. 6.3 lakhs

Concept used:

Divide the profit according to ratio of investment

Calculations:

Let money invests by A and B be 5x and 6x respectively

Total money invests by A in first 4 months = 5x × 4 = 20x

Total money invests by B in first 4 months = 6x × 4 = 24x

According to the question,

After 4 months money invests by A = 5x × 4/5 = 4x

After 4 months money invest by B = 6x × (100 + 100/300)

⇒ 6x × 4/3 = 8x

Total money invests by A in last 8 months = 4x × 8 = 32x

Total money invests by B in last 8 months = 8x × 8 = 64x

Total money invests by A in a year = 20x + 32x = 52x

Total money invests by B in a year = 24x + 64x = 88x

Ratio of money invests by A and B = 52x ∶ 88x

⇒ 13 ∶ 22

B’s profit = (6,30,000/35) × 22 = 3,96,000

∴ Share of B is 3.96 lakh.

7. A, B and C started a business. Twice the investment of A is equal to thrice the investment of B and also five times the investment of C. If the total profit after a year is Rs. 15.5 lakhs, then the share of B in the profit is (in Rs. lakhs):

A, B और C एक व्यवसाय प्रारंभ करते हैं। A के निवेश का दोगुना B के निवेश के तीन गुना और साथ ही C के निवेश के पांच गुना के बराबर है। यदि एक वर्ष के बाद कुल लाभ 15.5. लाख रुपये है, तो लाभ में B का हिस्सा क्या है: (लाख रुपये में)

Option”A” is correct

Twice the investment of A = Thrice the investment of B = Five times the investment of C

Total profit = Rs. 15.5 lakhs

Concept used:

Profit will be directly proportional to amount invested if time period is same

Calculation:

2A = 3B = 5C

L.C.M of 2, 3 and 5 = 30

So, A = 30/2 = 15

⇒ B = 30/3 = 10

⇒ C = 30/5 = 6

Total profit = 15 + 10 + 6 = 31

Share of B = (10/31) × 15.5 lakhs

⇒ Rs. 5 lakhs

∴ The share of B is Rs. 5 lakhs

8. Teena, Reena and Sheena start a business with investment of respectively ₹ 24000, ₹ 28000 and ₹ 20000. Teena invests for 8 months, Reena invest for 10 months and Sheena invests for one year. If the total profit at the end of year is ₹ 25810, then what is the share of Teena?

टीना, रीना और शीना क्रमशः ₹ 24000, ₹ 28000 और ₹ 20000 के निवेश के साथ एक व्यवसाय प्रारंभ करती हैं। टीना 8 महीनों के लिए, रीना 10 महीनों के लिए और शीना एक वर्ष के लिए निवेश करती है। यदि वर्ष के अंत में कुल लाभ ₹ 25810 है, तो टीना का हिस्सा क्या है?

Option”A” is correct

Teena, Reena and Sheena start a business with investment of respectively ₹ 24000, ₹ 28000 and ₹ 20000

Teena invests for 8 months, Reena invest for 10 months and Sheena invests for one year.

Total Profit = 25810

Concept:

Ratio in which profit divides = Sum of money invested by individual × Duration for which money is invested.

Calculation:

Ratio in which profit divides = 24000 × 8 : 28000 × 10 : 20000 × 12

⇒ Ratio = 24 × 8 : 28 × 10 : 20 × 12

⇒ Ratio = 24 : 35 : 30

Share of Teena

⇒ 25810 × 24/(24 + 35 + 30)

⇒ 25810 × 24/89

⇒ 290 × 24

⇒ Rs. 6960

∴ The share of teena is Rs. 6960.

9.P, Q, and R invest Rs. 14000, Rs. 18000 and Rs. 24000 respectively to start a business. If the profit at the end of the year is Rs. 25480, then what is the difference between the profit share of P and Q?

P, Q और R एक व्यवसाय शुरू करने के लिए क्रमशः 14000 रुपये, 18000 रुपये और 24000 रुपये का निवेश करते हैं। यदि एक वर्ष के अंत में लाभ 25480 रुपये है, तो P और Q के लाभ के हिस्से के बीच अंतर क्या है?

Option”C” is correct

P invests = Rs. 14000

Q invests = Rs. 18000

R invests = Rs. 24000

Profit = 25480

Concept:

The ratio of profit between P, Q and R will be the same as the ratio between the amount invested by them

Calculation:

P : Q : R = 14000 : 18000 : 24000

⇒ 7 : 9 : 12

Share of P = (7/28) × 25480 = 6370

Share of Q = (9/28) × 25480 = 8190

∴ Difference between the share of P and Q = 8190 – 6370 = Rs. 1820

10. Mohit and Sumit start a business with investment of ₹ 74000 and ₹ 96000 respectively. If at the end of the year they earn profit in the ratio of 5 : 8, then what will be ratio of the time period for which they invest their money?

मोहित और सुमित क्रमशः 74000 रुपये और 96000 रुपये के निवेश के साथ एक व्यवसाय शुरू करते हैं। यदि वर्ष के अंत में वे 5 : 8 के अनुपात में लाभ कमाते हैं, तो उस समय अवधि का अनुपात क्या होगा जिसके लिए वे अपने पैसे का निवेश करते हैं?

Option”D” is correct

Formula used:

Profit = investment × Time period

Calculation:

Let T1 and T2 be time periods of Mohit and Sumit respectively

5 = 74000 × T1

T1 = 5/74000

8 = 96000 × T2

T2 = 8/96000

Ratio of T1/T2 = (5/74000)/(8/96000) = 30: 37

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