11.K, L and M invest sum in the ratio 15 : 20 : 27 respectively. If they earned total profit of Rs. 10230 at the end of year, then what is the difference between share of K and L?

K, L और M क्रमशः 15 : 20 : 27 के अनुपात में धनराशि का निवेश करते हैं। यदि उन्होंने वर्ष के अंत में 10230 रुपये का कुल लाभ अर्जित किया, तो K और L के हिस्सों के बीच अंतर क्या है?


Option”D” is correct

K, L and M invest sum in the ratio = 15: 20: 27

Total profit earned = Rs. 10230

FORMULA USED:

Profit = Sum invested × Time period

CALCULATION:

As they all invested for same time period

Share of K = (15/62) × 10230 = Rs. 2475

Share of L = (20/62) × 10230 = Rs. 3300

∴ Difference between share of K and L = 3300 – 2475 = Rs. 825

12. A and B starts a business with investment of Rs. 28000 and Rs. 42000 respectively. A invests for 8 months and B invests for one year. If the total profit at the end of year is Rs. 21125, then what is the share of B?

A और B क्रमशः रु 28000 और रु 42000 के निवेश के साथ एक व्यवसाय शुरू करते हैं। A 8 महीने के लिए और B एक साल के लिए निवेश करता है। यदि वर्ष के अंत में कुल लाभ रु 21125 है, तो फिर B का हिस्सा क्या है?


Option”A” is correct

A’s investment = Rs. 28000 for 8 months

B’s investment = Rs. 42000 for 12 months

Total profit = Rs. 21125

Formula used:

Profit ratio = Investment ratio × Time (in months)

Calculation:

Profit of A/Profit of B = 28000 × 8/(42000 × 12)

⇒ Profit of A/Profit of B = 4/9

Let the profit of A be 4x and profit of B be 9x

So 13x = 21125

⇒ x = 1625

∴ Profit share of B = 9x = 9 × 1625 = Rs. 14625

13. A and B started a partnership business investing in the ratio of 2 : 5. C joined them after 3 months with an amount equal to 4/5th of B. What was their profit (in Rs.) at the end of the year if A got Rs. 16,800 as his share?

A और B ने 2 : 5 अनुपात में निवेश करके साझेदारी में एक व्यवसाय शुरू किया। C उनसे 3 माह बाद B की 4/5 राशि निवेश के साथ जुड़ा। यदि वर्ष  के अंत में A को 16,800 रुपये की हिस्सेदारी प्राप्त हुई तो उनका लाभ (रुपये में) क्या था?


Option”C” is correct

Ratio of A : B share in partnership is 2 : 5 

C joined them after 3 months with 4/5th amount of B 

Concept used :

Person’s share = Investment × time period of investment 

Calculations :

Let the amount of A be 2x 

Let the amount of B be 5x 

Amount of C = 4/5 of 5x = 4x 

Share of A = 2x × 12 = 24x        (A worked for whole year or 12 months)

Share of B = 5x × 12 = 60x        (worked for whole year)

Share of C = 4x × 9 = 36x          (worked 3 months less than A and B)

Now, ratio of shares

A : B : C = 24x : 60x : 36x 

⇒ 2 : 5 : 3 

Now total profit will be,

A’s share = (2/10) of total profit

Total profit = 5 × 16800 

⇒ 84000 rupees 

∴ total profit will be 84000 rupees

14. Three partners A, B and C divide Rs. 2,21,000 amongst themselves in such a way that if Rs. 2,000, Rs. 3,000 and Rs. 4,000 are removed from the sums that A, B and C received, respectively, then the share of the sums that they will get are in the ratio 11 : 18 : 24. How much (in Rs.) did B receive?

तीन साझेदार A, B और C, 2,21,000 रुपये को आपस में इस तरह से विभाजित करते हैं कि यदि 2,000 रुपये, 3,000 रुपये और 4,000 रुपये को क्रमशः A, B और C से प्राप्त धनराशी से निकाल दिया जाता है, तो धनराशी का हिस्सा वे 11: 18: 24 के अनुपात में प्राप्त करते हैं। B को कितनी धनराशी प्राप्त होती है?


Option”D” is correct

An amount of Rs. 2,21,000 among three partners A, B and C

The amount removed from A is Rs. 2,000

The amount removed from B is Rs. 3,000

The amount removed from C is Rs. 5,000

The ratio of divided sums is 11 : 18 : 24

Calculations:

Let the amount received by A be 11x

Let the amount received by B be 18x

Let the amount received by C be 24x

The total removed amount from A, B and C is

⇒ 2000 + 3000 + 4000

⇒ 9000

The total amount received by A, B, and C is

⇒ 221000 – 9000

⇒ 212000

Total ratio of amount is

⇒ 11x + 18x + 24x

⇒ 53x

According to question, we have

⇒ 53x = 212000

⇒ x = 212000/53

⇒ x = 4000

Amount received by B is 18x = 18 × 4000 = 72000

Total amount received by B is 72000 + 3000 = 75000

∴ The total amount received by B is Rs. 75,000

15. 3 friends A, B and C are working in a company. The salary of A is Rs. 45000 per month. C’s monthly salary is 3/5 of B’s monthly salary. B’s monthly salary is double of A’s monthly salary. What is the total salary of A, B and C per month ?

3 दोस्त A, B और C एक कंपनी में काम कर रहे हैं। A का वेतन 45000 रुपये प्रति माह है। C का मासिक वेतन B के मासिक वेतन का 3/5 है। B का मासिक वेतन A के मासिक वेतन से दोगुना है। A, B और C का प्रति माह कुल वेतन कितना है?


Option”C” is correct

⇒ A’s salary = Rs.45000

Calculation:

⇒ B’s salary = 45000 × 2 = Rs.90000

⇒ C’s salary = 90000 × 3/5 = Rs.54000

∴ Total salary of A, B and C = 90000 + 45000 + 54000 = Rs.1,89,000

16. A and B started a business investing amounts of Rs. 92,500 and Rs. 1,12,500 respectively. If B’s share in the profit earned by them is Rs. 9,000, what is the total profit (in Rs.) earned by them together?

A और B ने क्रमशः 92,500 रुपये और 1,12,500 रुपये की राशि से व्यवसाय शुरू किया। यदि उनके द्वारा अर्जित लाभ में B का हिस्सा 9,000 रुपये है, तो उन दोनों द्वारा अर्जित किया हुआ कुल लाभ (रुपये में) कितना है?


Option”D” is correct

Investment of A  = Rs. 92,500

Investment of B = Rs. 1,12,500

B’s share in profit = Rs. 9,000

Concept used:

If time of investment is equal for A and B then, ratio of profit earned by A and B is same as the ratio of investment done.

Calculations:

Ratio of profit = 92,500 : 1,12,500

⇒ 37 : 45

Let total profit be y.

B’s share in the profit = {45/(45 + 37)} × y

⇒ (45/82) × y = 9,000

⇒ y = 7,38,000/45

⇒ y = 16,400

∴ The total profit earned by them together is Rs. 16,400

17. A, B and C started a business investing amounts of Rs. 13,750, Rs. 16,250 and Rs. 18,750 respectively. lf B’s share in the profit earned by them is Rs. 5,200. what is the difference in the profit (in Rs.) earned by A and C ?

A, B और C ने क्रमशः 13,750 रुपये, 16,250 रुपये और 18,750 रुपये की राशि निवेश कर एक व्यवसाय शुरू किया। उनके द्वारा अर्जित लाभ में यदि B का भाग 5,200 रुपये है। A और C द्वारा अर्जित लाभ (रुपये में) में क्या अंतर है?


Option”B” is correct

A, B and C started a business investing amounts of Rs. 13,750, Rs. 16,250 and Rs. 18,750 respectively.

Concept Used:

In the partnership business profit is distributed in the ratio of their Investment.

Calculation:

Ratio of investment of A, B and C is 13750 : 16250 : 18750

⇒ 11 : 13 : 15

B’s share is 13 units → 5200

⇒ 1 unit → 400

Difference in the profit earned by A and C is (15 – 11) = 4 unit

1 unit → Rs. 400

⇒ 4 unit → Rs. 400 × 4 = Rs. 1600

∴ The difference in the profit earned by A and C is Rs. 1600.

18. Ramesh started a business investing a sum of Rs. 40,000. Six months later, Kevin joined by investing Rs. 20,000. If they make a profit of Rs. 10,000 at the end of the year, how much is the share of Kevin?

रमेश ने 40,000 रु. का निवेश करके एक व्यवसाय शुरू किया। छह महीने बाद, केविन 20,000 रु. का निवेश करके व्यवसाय में जुड़ गया। यदि वे एक वर्ष के अंत में 10,000 रु. का लाभ कमाते हैं, तो केविन की हिस्सेदारी कितनी है?


Option”A” is correct

Ramesh’s investment = Rs. 40000

Kevin’s investment = Rs. 20000

Total profit at the end of the year = Rs. 10000

Ramesh’s time period of investment = 12 months

Kevin’s time period of investment = 6 months

Formula used:

(Ramesh’s profit) ∶ (Kevin’s profit) = (Ramesh’s capital × Time period of investment) ∶ (Kevin’s capital × Time period of investment)

Calculations:

Ratio of their profit = (40000 × 12) ∶ (20000 × 6)

⇒ 480000 ∶ 120000

⇒ 4 ∶ 1

Ramesh’s profit = 4x

Kevin’s profit = x

Total profit = 4x + x

⇒ 5x = 10000

⇒ x = Rs. 2000 

∴ The share of Kevin in the total profit is Rs. 2000

19. A, B and C invested capital in the ratio 5 : 7 : 4, the timing of their investments being in the ratio x : y : z. If their profits are distributed in the ratio 45 : 42 : 28, then x : y : z = ? 

A, B और C ने 5 ∶ 7 ∶ 4 के अनुपात में पूंजी लगाई, उनके निवेश का समय x ∶ y ∶ z के अनुपात में है। यदि उनका लाभ 45 ∶ 42 ∶ 28 के अनुपात में वितरित किया जाता है, तो x: y: z = ?


Option”D” is correct

The ratio of investment of A, B, and C is 5 ∶ 7 ∶ 4

The timing ratio of A, B, and C is x ∶ y ∶ z

The profits distribution ratio is 45 ∶ 42 ∶ 28

Concept used:

Profits distributed in the ratio of investment ×  time

Calculation:

                                    A                      B                      C

Investment                  5                       7                      4

Time                            x                       y                      z

—————————————————————————-

Profits Distribution      45                   42                     28

⇒ 5x = 45 ; 7y = 42 ; 4z = 28

⇒ x = 9 ; y = 6 ; z = 7

∴ x ∶ y ∶ z = 9 ∶ 6 ∶ 7

20. A is twice as good as workman as B and together they finish a piece of work in 16 days. In how many days will A alone finish the work ?X and Y enter into a partnership with capital in the ratio 3 ∶ 5 After 5 months X adds 50% of his capital, while Y withdraws 60% of his capital. What is the share (in Rs. lakhs) of X in the annual profit of Rs. 6.84 lakhs?

X और Y साझेदारी में 3 ∶ 5 के अनुपात में पूंजी निवेश करते हैं 5 महीने के बाद X अपनी पूंजी का 50% और लगाता है, जबकि Y अपनी पूंजी का 60% निकाल लेता है। 6.84 लाख रुपये के वार्षिक लाभ में X का हिस्सा (लाख रुपये में) क्या है?


Option”C” is correct

X and Y enter into partnership with capital in the ratio = 3 ∶ 5

After 5 months,

X’s capital = 150% of initial investment of X

Y’s capital = 40% of initial investment of Y

Annual profit = Rs. 6.84 lakhs

Formula used:

(X’s profit) ∶ (Y’s profit) = (X’s capital × Time period of investment) ∶ (Y’s capital × Time period of investment)

Calculations:

Let X’s and Y’s initial investment for the first 5 months be 30 and 50

After 5 months,

X’s capital for next 7 months = (150/100) × 30 = 45

Y’s capital for next 7 months = (40/100) × 50 = 20

(X’s profit)/(Y’s profit) = [(30 × 5) + (45 × 7)]/[(50 × 5) + (20 × 7)]

⇒ (150 + 315)/(250 + 140)

⇒ 465/390

⇒ 31/26

Total profit = 31 + 26 = 57 units

⇒ (X’s profit)/(Total profit) = 31/57

⇒ (X’s profit)/6.84 = 31/57

⇒ X’s profit = (31/57) × 6.84

⇒ X’s profit = 3.72

∴ The profit earned by X is Rs. 3.72 lakhs

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