1. Two friends invested Rs.1500 and Rs. 2500 in a business. They earned a profit of Rs. 800. One-half of the profit was divided equally between them and the other half was divided in proportion to their capitals. How much did each of them receive ?
a) Rs. 350 and Rs. 450
b) Rs. 360 and Rs. 440
c) Rs. 370 and Rs. 430
d) Rs. 375 and Rs. 425
Explanation:
$$\eqalign{ & {\text{Ratio of shares}} = 1500:2500 \cr & = 3:5 \cr & {\text{Share of first friend}} = {\text{Rs}}{\text{.}}\left[ {\frac{{400}}{2} + \left( {400 \times \frac{3}{8}} \right)} \right] \cr & = {\text{Rs}}.\left( {200 + 150} \right) \cr & = {\text{Rs}}{\text{. 350}} \cr & {\text{Share of second friend}} = {\text{Rs}}{\text{.}}\left[ {\frac{{400}}{2} + \left( {400 \times \frac{5}{8}} \right)} \right] \cr & = {\text{Rs}}.\left( {200 + 250} \right) \cr & = {\text{Rs}}{\text{. 450}} \cr} $$
2. Three persons stared a placement business with a capital of Rs. 3000. B invests Rs. 600 less than A and C invests Rs. 300 less than B. What is B's share in a profit of Rs. 886 ?
a) Rs. 443
b) Rs. 354.40
c) Rs. 265.80
d) Rs. 177.20
Explanation: Let A's capital = Rs. x
B's capital = Rs. (x - 600)
C's capital = Rs. (x - 600) - 300 = Rs. (x - 900)
∴ x + (x - 600) + (x - 900) = 3000
3x = 4500
x = 1500
$$\eqalign{ & {\text{So, A}}:{\text{B}}:{\text{C}} = 1500:900:600 \cr & = 5:3:2 \cr & {\text{B's share}} = {\text{Rs}}{\text{.}}\left( {886 \times \frac{3}{{10}}} \right) \cr & = {\text{Rs}}{\text{. 265}}{\text{.80}} \cr} $$
3. X and Y are partners in a business. They invest in the ratio 5 : 6, at the end of 8 months X withdraws his capital. If they receive profits in the ratio of 5 : 9. Find how long Y's investment was used ?
a) 12 months
b) 10 months
c) 15 months
d) 14 months
Explanation: Let Y's investment is used for T months → Now by using formula
$$\eqalign{ & \frac{{5 \times 8}}{{6 \times {{\text{T}}_2}}} = \frac{5}{9} \cr & {\text{T}} = 12{\text{ months}} \cr} $$
4. Four milkmen rented a pasture. M put to graze 16 cows for 3 months and N 20 cows for 4 months, O 18 cows for 6 months and P 42 cows for 2 months. If M's share of rent be Rs. 2400, the rent paid by O is ?
a) Rs. 3200
b) Rs. 4200
c) Rs. 4000
d) Rs. 5400
Explanation: M graze 16 cows for 3 months
N graze 20 cows for 4 months
O graze 18 cows for 6 months
P graze 42 cows for 2 months
Ration of Rent = M : N : O : P
= (16 × 3) : (20 × 4) : (18 × 6) : (42 × 2)
= 48 : 80 : 108 : 84
= 12 : 20 : 27 : 21
$$\eqalign{ & {\text{12 units}} = {\text{Rs}}{\text{. 2400}} \cr & {\text{1 unit}} = \frac{{2400}}{{12}} \cr & 27{\text{ units}} = \frac{{2400 \times 27}}{{12}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}5400 \cr} $$
5. Shankar starts a business with an investment of Rs. 120000. After three months, Aniket joined him with an invesment of Rs. 190000. They earned a profit of Rs. 1750000 after one year. What is Aniket's share in the profit ?
a) Rs. 800000
b) Rs. 850000
c) Rs. 900000
d) Rs. 950000
Explanation:
$$\eqalign{ & {\text{Shankar}}:{\text{Aniket}} = \left( {120000 \times 12} \right):\left( {190000 \times 9} \right) \cr & = 1440000:1710000 \cr & = 16:19 \cr & {\text{Aniket's share}} = {\text{Rs}}{\text{.}}\left( {1750000 \times \frac{{19}}{{35}}} \right) \cr & = {\text{Rs. }}{\text{950000 }} \cr} $$
6. Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is
a) Rs. 200
b) Rs. 300
c) Rs. 400
d) Rs. 500
Explanation: Let C = x
B = $$\frac{{\text{x}}}{2}$$
A = $$\frac{{\text{x}}}{4}$$
A : B : C = 1 : 2 : 4
C's share = $${\text{Rs}}{\text{.}}\left( {\frac{4}{7} \times 700} \right) = 400$$
7. Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is
a) Rs. 9600
b) Rs. 8500
c) Rs. 8450
d) Rs. 8400
Explanation: Ratio of their shares = 22500 : 35000
= 9 : 14
Deepak's share
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {13800 \times \frac{{14}}{{23}}} \right) \cr & = {\text{Rs}}{\text{. 8}}400 \cr} $$
8. A started a business with Rs. 21,000 and is joined afterwards by B with Rs. 36,000. After how many months did B join if the profits at the end of the year are divided equally?
a) 4
b) 5
c) 6
d) 7
Explanation: Suppose B joined after x months
21000 × 12 = 36000 × (12 - x)
36x = 180
x = 5
9. Nirmal and Kapil started a business investing Rs. 9000 and Rs. 12000 respectively. After 6 months, Kapil withdrew half of his investment. If after a year, the total profit was Rs. 4600, what was Kapil’s share initially ?
a) Rs. 2300
b) Rs. 2400
c) Rs. 2500
d) None of above
Explanation: Nirmal : Kapil = 9000 × 12 : (12000 × 6 + 6000 × 6)
= 1 : 1
Kapils share
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {4600 \times \frac{1}{2}} \right) \cr & = {\text{Rs}}{\text{. 2300}} \cr} $$
10. Manoj received 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.120000 for 6 months, whereas Ramesh invested his amount for the whole year, what was the amount invested by Ramesh
a) Rs. 2000
b) Rs. 30000
c) Rs. 4000
d) Rs. 5000
Explanation: Suppose Ramesh invested Rs. x.
Manoj : Ramesh = 120000 × 6 : x × 12.
$$\eqalign{ & \frac{{720000}}{{12{\text{x}}}}:\frac{{6000}}{{3000}} \cr & {\text{x}} = \frac{{720000}}{{24}} \cr & {\text{x}} = 30000 \cr} $$