1. Samaira, Mahira and Kiara rented a set of DVDs at a rent of Rs. 578. If they used it for 8 hours, 12 hours and 14 hours respectively, what is Kiara's share of rent to be paid ?

a) Rs. 192

b) Rs. 204

c) Rs. 215

d) Rs. 238

Explanation:

$$\eqalign{ & {\text{Ratio of shares}} \cr & = 8:12:14 \cr & = 4:6:7 \cr & {\text{Kiara's share}} = {\text{Rs}}{\text{.}}\left( {578 \times \frac{7}{{17}}} \right) \cr & = {\text{Rs. }}{\text{238}} \cr} $$

2. P, Q and R invested Rs. 45000, Rs. 70000 and Rs. 90000 respectively to start a business. At the end of 2 years, they earned a profit of Rs.164000. What will be Q's share in the profit ?

a) Rs. 36000

b) Rs. 56000

c) Rs. 64000

d) Rs. 72000

Explanation:

$$\eqalign{ & {\text{P}}:{\text{Q}}:{\text{R}} \cr & = 45000:70000:90000 \cr & = 9:14:18 \cr & {\text{Q's share}} = {\text{Rs}}{\text{.}}\left( {164000 \times \frac{{14}}{{41}}} \right) \cr & = {\text{Rs. }}{\text{56000}} \cr} $$

3. A working partner gets 20% as his commission of the profit after his commission is paid. If the working partner's commission is Rs. 8000, then what is the total profit in the business ?

a) Rs. 47000

b) Rs. 45000

c) Rs. 48000

d) None of these

Explanation: Let the total profit = Rs. k

Remaining profit after paying 20% working

Partner's commission = (k - 8000)

$$\eqalign{ & \therefore \,\left( {k - 8000} \right) \times \frac{{20}}{{100}} = 8000 \cr & k = 48000 \cr & {\text{ Total profit}} = {\text{Rs}}{\text{. 48000}} \cr} $$

4. We have to divided a sum of Rs. 13950 among three persons A, B and C. B must get the double of A's share and C must get Rs. 50 less than the double of B's share. The share of A will be ?

a) Rs. 1950

b) Rs. 1981.25

c) Rs. 2000

d) Rs. 2007.75

Explanation: Let the share of A = Rs. x

$$\eqalign{ & {\text{A}}:{\text{B}}:{\text{C}} \cr & {\text{Capital}} \to x:2x:\left( {4x - 50} \right) \cr & \left( {x + 2x + 4x - 50} \right) = 13950 \cr & 7x - 50 = 13950 \cr & 7x = 14000 \cr & x = 2000 \cr & {\text{Share of A}} = {\text{Rs}}{\text{. 2000}} \cr} $$

5. Prakash, Sachin and Anil started a business jointly investing Rs. 11 lakh, Rs. 16.5 lakh and Rs.8.25 lakh respectively. The profit earned by them in the business at the end of 3 years was Rs. 19.5 lakh. What will be 50% of Anil's share in the profit ?

a) Rs. 2.25 lakh

b) Rs. 2.50 lakh

c) Rs. 3.75 lakh

d) Rs. 4.50 lakh

Explanation:

$$\eqalign{ & {\text{Ratio of shares}} \cr & = 11:16.5:8.25 \cr & = 4:6:3 \cr & {\text{Anil's share}} = {\text{Rs}}{\text{.}}\left( {19.5 \times \frac{3}{{13}}} \right) \cr & = {\text{Rs. }}{\text{4}}{\text{.5 lakh}} \cr & {\text{Required amount}} = 50\% {\text{ of 4}}{\text{.5 lakh}} \cr & = {\text{Rs. }}{\text{2}}{\text{.25 lakh}} \cr} $$

6. Arun started a business investing Rs. 38000. After 5 months Bakul joined him with a capital of Rs. 55000. At the end of the year the total profit was Rs. 22000. What is the approximate difference between the share of profits Arun and Bakul ?

a) Rs. 1007

b) Rs. 1192

c) Rs. 1568

d) Rs. 1857

Explanation:

$$\eqalign{ & {\text{Arun}}:{\text{Bakul}} = \left( {38000 \times 12} \right):\left( {55000 \times 7} \right) \cr & = 456000:385000 \cr & = 456:385 \cr & {\text{Required difference}} = {\text{Rs}}{\text{.}}\,\left[ {22000 \times \left( {\frac{{456}}{{841}} - \frac{{385}}{{841}}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\left( {22000 \times \frac{{71}}{{841}}} \right) \cr & = {\text{Rs. }}{\text{1857}}{\text{.31}} \cr & = {\text{Rs. }}{\text{1857 }} \cr} $$

7. Goutam started a business with a sum of Rs. 60000. Jatin joined him 8 months later with a sum of Rs. 35000. At what respective ratio will the two share of profit after two years ?

a) 2 : 1

b) 3 : 1

c) 18 : 7

d) 37 : 14

Explanation:

$$\eqalign{ & {\text{Gautam}}:{\text{Jatin}} = \left( {6000 \times 12} \right):\left( {35000 \times 8} \right) \cr & = 720000:280000 \cr & = 18:7 \cr} $$

8. Simran started a software business by investing Rs. 50000. After six months, Nanda joined her with a capital of Rs. 80000. After 3 years, they earned a profit of Rs. 24500. What was Simran's share in the profit ?

a) Rs. 9423

b) Rs. 10250

c) Rs. 12500

d) None of these

Explanation:

$$\eqalign{ & {\text{Simran}}:{\text{Nanda}} = \left( {50000 \times 36} \right):\left( {80000 \times 30} \right) \cr & = 1800000:2400000 \cr & = 3:4 \cr & {\text{Simran's share}} = {\text{Rs}}{\text{.}}\left( {24500 \times \frac{3}{7}} \right) \cr & = {\text{Rs. }}{\text{10500 }} \cr} $$

9. Dilip, Ram and Avtar started a shop by investing Rs. 2700, Rs. 8100 and Rs. 7200 respectively. At the end of one year, the profit earned was distributed. If Ram's share was Rs. 3600, what was their total profit ?

a) Rs. 8000

b) Rs. 10800

c) Rs. 11600

d) Data inadequate

Explanation:

$$\eqalign{ & {\text{Dilip}}:{\text{Ram}}:{\text{Avtar}} \cr & = 2700:8100:7200 \cr & = 3:9:8 \cr & {\text{Let the total profit be Rs}}.\,x \cr & {\text{Ram's share}} = {\text{Rs}}{\text{.}}\,\left( {\frac{9}{{20}}x} \right) \cr & \therefore \frac{9}{{20}}x = 3600 \cr & x = \left( {\frac{{3600 \times 20}}{9}} \right) \cr & x = 8000 \cr & {\text{Total profit}} = {\text{Rs}}{\text{. 8000}} \cr} $$

10. Aman started a business investing Rs. 70000. Rakhi joined him after six months with an amount of Rs. 105000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?

a) 7 : 6 : 10

b) 12 : 15 : 16

c) 42 : 45 : 56

d) Cannot be determined

Explanation: Aman : Rakhi : Sagar

= (70000 × 36) : (105000 × 30) : (140000 × 24)

= 12 : 15 : 16