1. In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs. 157300 was their profit, how much amount did B receive?
a) Rs. 48400
b) Rs. 48600
c) Rs. 48000
d) Rs. 48200
Explanation:
Assume that investment of C = x
Then, investment of A = 2x
Investment of B = $$\frac{{2{\text{A}}}}{3}$$ = $$\frac{{4{\text{x}}}}{3}$$ (since ratio of investment of A : B = 2 : 3 i.e B = $$\frac{{2{\text{A}}}}{3}$$)
A : B : C
= 2x : $$\frac{{4{\text{x}}}}{3}$$ : x
= 2 : $$\frac{4}{3}$$ : 1
= 6 : 4 : 3
$$\eqalign{ & {\text{B's Share}} \cr & = 157300 \times \frac{4}{{6 + 4 + 3}} \cr & = 157300 \times \frac{4}{{13}} \cr & = 12100 \times 4 \cr & = {\text{Rs}}{\text{. 48400}} \cr} $$
2. A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?
a) Rs. 8000
b) Rs. 7500
c) Rs. 8500
d) Rs. 9000
Explanation:
Let B's capital be Rs. x
∴ A's share in 12 months = 3500 × 12
And, B's share in 7 months = 7x
$$\eqalign{ & {\text{Then}},\, {\frac{{3500 \times 12}}{{7x}} = \frac{2}{3}} \cr & \Rightarrow 14x = 126000 \cr & \Rightarrow x = 9000 \cr} $$
3. A, B, C subscribe Rs. 5,00,000 for a business. A subscribes Rs. 40,000 more than B and B Rs. 50,000 more than C. Out of a total profit of Rs. 3,50,000 A receives:
a) Rs. 84,000
b) Rs. 1,47,000
c) Rs. 1,36,000
d) Rs. 1,19,000
Explanation:
$$\eqalign{ & {\text{Let}}\,C = x \cr & {\text{Then,}}\,{\text{B}} = x + 50000\,{\text{and}} \cr & {\text{A}} = x + 50000 + 40000 \cr & \,\,\,\,\,\,\,\, = x + 90000 \cr & So,\,x + x + 50000 + x + 90000 = 500000 \cr & \Rightarrow 3x = 360000 \cr & \Rightarrow x = 120000 \cr & {\text{A:B:C}} = 210000:170000:120000 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 21:17:12 \cr & \therefore {\text{A's}}\,{\text{share}} \cr & = Rs.\,\left( {350000 \times \frac{{21}}{{50}}} \right) \cr & = Rs.\,1,47,000 \cr} $$
4. Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?
a) Rs. 890
b) Rs. 1780
c) Rs. 1335
d) Rs. 1602
Explanation:
$$\eqalign{ & {\text{Arun}}\,{\text{:}}\,{\text{Kamal}}\,{\text{:}}\,{\text{Vinay}} \cr & = \left( {8000 \times 6} \right):\left( {4000 \times 8} \right):\left( {8000 \times 8} \right) \cr & = 48:32:64 \cr & = 3:2:4 \cr & \therefore {\text{Kamal's}}\,{\text{share}} \cr & = Rs.\,\left( {4005 \times \frac{2}{9}} \right) \cr & = Rs.\,890 \cr} $$
5. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
a) 5 : 7 : 8
b) 38 : 28 : 21
c) 20 : 49 : 64
d) None of these
Explanation:
$$\eqalign{ & {\text{Let their investments be}}\, \cr & Rs.\,x\,{\text{for}}\,{\text{14}}\,{\text{months}},\, \cr & Rs.\,y\,{\text{for}}\,{\text{8}}\,{\text{months}}\,{\text{and}}\, \cr & Rs.\,z\,{\text{for}}\,{\text{7}}\,{\text{months}}\,{\text{respectively}}. \cr & {\text{Then}},\,14x:8y:7z = 5:7:8 \cr & {\text{Now}},\frac{{14x}}{{8y}} = \frac{5}{7} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,98x = 40y \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y = \frac{{49}}{{20}}x \cr & {\text{And}},\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,112x = 35z \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,z = \frac{{112}}{{35}}x = \frac{{16}}{5}x \cr & \therefore x:y:z \cr & = x:\frac{{49}}{{20}}x:\frac{{16}}{5}x \cr & = 20:49:64 \cr} $$
6. A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
a) Rs. 30
b) Rs. 50
c) Rs. 40
d) Rs. 45
Explanation:
$$\eqalign{ & A:B:C \cr & = \left( {10 \times 7} \right):\left( {12 \times 5} \right):\left( {15 \times 3} \right) \cr & = 70:60:45 \cr & = 14:12:9 \cr & \therefore {\text{C's rent}} = {\text{Rs}}{\text{.}}\left( {175 \times \frac{9}{{35}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}45 \cr} $$
7. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
a) Rs. 10,000
b) Rs. 7500
c) Rs. 9000
d) Rs. 9500
Explanation:
$$\eqalign{ & A:B:C \cr & = \left( {20000 \times 24} \right):\left( {15000 \times 24} \right):\left( {20000 \times 18} \right) \cr & = 4:3:3 \cr & \therefore {\text{B's}}\,{\text{share}} = Rs.\,\left( {25000 \times \frac{3}{{10}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,7500 \cr} $$
8. Sumit and Ravi started a business by investing Rs. 85000 and Rs. 15000 respectively. In what ratio the profit earned after 2 years be divided between Sumit and Ravi respectively.
a) 17 : 2
b) 17 : 4
c) 17 : 3
d) 17 : 1
Explanation:
Sumit : Ravi = 85000 : 15000 = 17 : 3
Important to note there that if both have invested for different period of times then we had to multiply with number of months to get the desired ratio.
9. A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:
a) Rs. 1537.50
b) Rs. 1500
c) Rs. 1425
d) Rs. 1576
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{total}}\,{\text{profit}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{100}} \cr & {\text{After}}\,{\text{paying}}\,{\text{to}}\,{\text{charity,}}\,{\text{A's}}\,{\text{share}} \cr & = Rs.\,\left( {95 \times \frac{3}{5}} \right) = Rs.\,57 \cr & {\text{If}}\,{\text{A's}}\,{\text{share}}\,{\text{is}}\,Rs.\,57, \cr & {\text{Total}}\,{\text{profit}} = Rs.\,100 \cr & {\text{If}}\,{\text{A's}}\,{\text{share}}\,Rs.\,855, \cr & {\text{Total}}\,{\text{profit}} \cr & = {\frac{{100}}{{57}} \times 855} \cr & = 1500 \cr} $$
10. A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
a) 6 : 10 : 5
b) 3 : 5 : 2
c) 3 : 5 : 5
d) Data inadequate
Explanation:
Let initial investment of A is 3x and B is 5x, then C investment is also 5x
A invested for 12 months, B invested for 12 months and C invested for 6 months.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6)
= 36 : 60 : 30
= 6 : 10 : 5