**Qu.1) X and Z invest capital in the ratio 2 : 1 while X and Y invest capital in the ratio 3 : 2. If their annual profit is Rs. 1,57,300 then what is Y’s share?**

**Sol**. Given: X : Z = 2×3:1×3

And X : Y = 3×2:2×2

Note: X will be same in both cases, hence new required ratio

Therefore, X: Y: Z = 6 : 4 : 3

According to the question, (6 + 4 + 3) units = Rs. 1,57, 300

13 units = Rs. 1,57,300

1 unit = Rs. 1,21,00

4 units = Rs. 1,2100 × 4 = Rs. 48,400 (since Y = 4x)

Ans. Therefore, Share of Y = Rs. 48,400

**Qu.2) X, Y and Z enter into a partnership. X invests 1/ 4part of total capital for one-fourth of the time. Y contributes one fifth of the capital for half of the time. Z contributes the remaining capital for the whole time. How should they share a profit of Rs. 1140?**

**Sol**. Let X invests a/4 for b/4 Month

Y invests a/5 for b/2 Month

Z invests = [a−(a/4 + a/5 )] for b months = 11a/ 20

Ratio of their investments = (a/4 × b/4):(a/5 x b/2):(11a/ 20 × b)

= 1/16: 1/10: 11/ 20

= 5: 8: 44

According to the question, (5 + 8+ 44) = Rs.1140

57 units = 1140

1 unit = 1140/ 57 = Rs, 20

**Ans. Profit of X = 20 x 5 = Rs. 100**

**Profit of Y = 20 x 8 = Rs. 160**

**Profit of Z = 20 x 44 = Rs. 880**

**Qu.3) Bhuvnesh, Rakesh and Pawan started a business with Rs.47,000. Bhuvnesh puts in Rs. 5,000 more than Rakesh and Rs.3,000 more than Pawan. The share of Bhuvnesh out of the profit of Rs.14,100 will be:**

**Sol**. Given: Total investment = Rs. 47, 000

Let amount invested by Pawan be Rs. X

Then amount invested by Rakesh = Rs. X + 3000

And amount invested by Bhuvnesh = Rs. X + 3000 + 5000

According to the question, X + X + 3000 + X + 3000 + 5000 = 47000

3X + 11000 = 47000

3X = 47000 – 11000

3X = 36000

X = 36000/ 3

X = 12000

Pawan amount =Rs. 12000, Rakesh = 12000 + 3000 = 15000

Bhuvnesh = !2000 + 3000 + 5000 = 20000

Their Ratio = P: R : B = 12: 15: 20

Since the time for which the amounts were invested was same for all the partners the ratio of amounts will be the ratio of profits

Therefore, share of Bhuvnesh out of total profit = [14100/ (20 + 10 + 15)] x 20

= Rs. 6000

**Ans. Bhuvnesh share = Rs. 6000**

**Qu.4) Bhuvnesh and Ankur enter into a partnership. At the end of 9 months Ankur withdraws but Bhuvnesh’s capitals is used for one month more. If they receive profit in the ratio 5 : 6, then the ratio of their capital is:**

**Sol**. Let Bhuvnesh’s Capital = Rs. X

Let Ankur’s Capital = Rs. Y

Now Acc. to question,

Bhuvnesh Capital C1 = Rs. X and time = 9 + 1 = 10 months and profit P1 = 5

Ankur Capital C2 = Rs. Y and time = 9 months and profit P2 = 6

Now, C1 T1 / C2 T2 = P1/ P2

X. 10 / Y. 9 = 5/ 6

X/ Y = 5. 9/ 6. 10 = 45/ 60

C1/ C2 = 3/ 4

**Ans. The ratio of their capital is 3: 4**

**Qu.5) Manoj, Pradeep and Chetan hired a car for Rs. 4,160. Manoj used it for 7 hours. Pradeep for 8 hours and Chetan used it for 11 hours. The rent shared by Manoj will be :**

**Sol**. Total cost of renting a car = Rs. 4,160

According to the question,

Manoj Pradeep chetan

Time of using car in hours 7 8 11

Here the ratio of time will be the ratio of rent each person has to pay.

ratio of rents to be paid 7 : 8 : 11

Rent shared by manoj = Total cost of renting a car x manoj time/ (sum of ratio of time of all 3)

= 4160 x 7/ (7 + 8 + 9)

= Rs, 1120

**Ans. The rent shared by Manoj will be Rs. 1120**

**Qu.6) A, B, C pasture in the same field, A has in it 10 oxen for 7 months, B has 12 oxen for 5 months and C has 15 oxen for 3 months. The rent is Rs 17.50. How much of the rent should each pay?**

**Sol.** Share of rent for A = 10 x 7 = 70

B = 12 x 5 = 60

C = 15 x 3 = 45

Ratio of their share of rent = 70: 60: 45 = 14: 12: 9 (14 + 12 + 9 = 35)

**Ans. A will pay = 17.50 x (14/ 35) = Rs.7**

** B will pay = 17.50 x (12/ 35) = Rs.6**

** C will pay =17.50 x (9/ 35) = Rs. 4.5**

**Qu.7) Manoj got Rs. 6000 as his share out of the total profit of Rs. 9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs. 20000 for 6 months, whereas Ramesh invested his amount for the whole year, the amount invested by Ramesh was:**

**Sol.** Given: total profit = Rs. 9000

Manoj share = Rs. 6000, therefore Ramesh share =Rs. 9000 – 6000 = Rs. 3000

Capital of Manoj = Rs. 20000

Time of investment of Manoj = 6 months, And that of Ramesh = 12 months

To find: Investment of Manoj = ?

Now, Let the investment made by Manoj to be A

Profit = Capital x time

Then, profit share will be,

6000/ 3000 = [20000 x 6]/ [A x 12]

A = 20000 x 6 x 3000/ 6000 x 12

A = Rs. 5000

**Ans. Amount invested by Ramesh is Rs. 5000**

**Qu.8) A and B enter into a partnership with Rs. 50,000 and Rs. 60,000 respectively. C joins them after x months contributing Rs. 70,000 and B leaves x months before the end of the year. If they share the profit in the ratio of 20: 18: 21, then find the value of x:**

**Sol. **Capital invested by A = Rs. 50,000 by B = Rs. 60,000 by C = Rs. 70,000

Profit ratio = 20: 18: 21

Time duration of A = 12 months

Time duration of B = (12 – x) months

Time duration of C = (12 – x) months

Profit = Capital x time

Ratio of their profit = A: B: C = 50000 x 12 : 60000 x (12 – x) : 70000 x (12 – x)

Let us consider the profit of A and B –

50000 x 12/ 60000 x (12 – x) = 20/ 18

60/ 6(12 – x) = 20/ 18

10/ (12 – x) = 20/ 18

9/ (12 – x) = 1

9 = 12 – x

x= 12 – 9

x= 3 months

**Ans. The value of x is 3 months.**

**Qu.9) A & B are two partners start a business by investing a capital of Rs. 25,000 and Rs. 35,000 and decide to share their profit according to their capital. Later C joins the business on a condition that they will distribute the profit equally (1:1:1) and for that C gives 2,20,000 to A & B. Find in which ratio A & B distribute that amount.**

**Sol**. Capital of A and B = 25000 and 35000

Capital of C = 2,20,000

Profit ratio = 1: 1: 1

Ratio of capital of A and B = 5: 7 (7+ 5 = 12)

Profit = 12

Now C wants to divide it equally

I.e.,. 12 will be divided into 3 equal parts having 4 parts each

Therefore, A: B: C = 5: 7 : C

Which should be = 4: 4: 4

For A 5 – 4 = 1 and for B 7 – 4 = 3, these 1 and 3 parts will go to C to make Profit ratio equal

I.e., 2,20,000/4 = 55000

1 part will go to A = Rs. 55,000

3 part will go to C = 55,000 x 3 = Rs. 1,65,000

**Ans. Hence required ratio will be 1: 3**

**Qu.10) A & B start a business with Rs. 50 and Rs. 45 respectively. After 4 months A withdraws half of his capital and B withdraws half capital after 6 months and C joins the business with a capital of Rs. 70 after 6 months. Find the profit sharing ratio.**

**Sol**. Capital invested by A = Rs. 50 and by B = Rs. 45

After 4 months A capital = 50/ 2 = Rs. 25

After 6 months B capital = 45/ 2 = Rs. 22.5

After 6 months capital = Rs. 70

Profit = Capital x time

A: B: C = 50 x 4 + 25 x 8 : 45 x 6 + 22.5 x 6 : 70 x 6

= 400 : 405 : 420

= 80: 81: 84

**Ans. The required profit ratio is 80: 81: 84.**