17. A and B entered into a partnership investing Rs.16000 and Rs.12000 respectively. After 3 months, A withdrew Rs.5000 while B invested Rs.5000 more. After 3 more months C joins the business with a capital of Rs.21,000. The share of B exceeds that of C, out of a total profit of Rs.26,400 after one year, by :
a. Rs.1200
b. Rs.2400
c. Rs.3600
d. Rs.4800

18. Jayant started a business, investing Rs.6000. Six months later Madhu joined him, investing Rs.4000. If they made a profit of Rs.5200 at the end of the year, how much be the share of Madhu ?
a. Rs.2080
b. Rs.1300
c. Rs.1800
d. Rs.2600

Answer: B

Explanation:
Ratio of their shares $6000 \times 12:4000 \times 6 = 3:1$
Madhu's share = Rs.$\left( {5200 \times \displaystyle\frac{1}{4}} \right)$ = Rs.1300

19. A,B,C subscribe Rs.47000 for a business. A subscribes Rs.7000 more than B and B Rs.5000 more than C. Out of a total profit of Rs.9400, B receives:
a. Rs.4400
b. Rs.3000
c. Rs.2000
d. Rs.1737.90

Answer: B

Explanation:
Suppose C invests Rs.x
Then, B's investment = Rs.(x + 5000)
And A's investment = Rs.(x + 12000)
x + x + 5000 + x + 12000 = 47000
(or) x = 10000
Thus, A:B:C = 22000 : 15000: 10000
= 22 : 15 : 10
B's share = Rs.$\left( {9400 \times \displaystyle\frac{{15}}{{47}}} \right)$ = Rs.3000

20. 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, total profit is :
a. Rs.1576
b. Rs.1537.50
c. Rs.1500
d. Rs.1425

Answer: C

Explanation:
Let the total profit be Rs.100
After paying to charity, A's share
= Rs.$\left( {95 \times \displaystyle\frac{3}{5}} \right)$=Rs.57
If A's share is Rs.57, total profit = Rs.100
If A's share is Rs.855, total profit = Rs.$\left( {855 \times \displaystyle\frac{{100}}{{57}}} \right)$=Rs.1500

21. A,B,C enter into a partnership with shares in the ratio $\displaystyle\frac{7}{2}:\displaystyle\frac{4}{3}:\displaystyle\frac{6}{5}$. After 4 months, A increases his share by 50%. If the total profit at the end of one year is Rs.21600, then B's share in the profit is :
a. Rs.2100
b. Rs.2400
c. Rs.3600
d. Rs.4000

Answer: D

Explanation:
Let Arvind's age be x years
Given Ratio = $\displaystyle\frac{7}{2}:\displaystyle\frac{4}{3}:\displaystyle\frac{6}{5}$=105:40:36 (multiply the entire ratio by LCM (2, 3, 5) = 30)
Let them initially invest Rs.105, Rs.40 and Rs.36 respectively.
As A increase his capital by 50% after 4 months, his capital for the first 4 months is 105 and for the remaining 8 months is 150% (105).
Ratio of investments = $(105 \times 4 + (150\% {\rm\text{ of 105)}} \times 8)$ : $(40 \times 12) : (36 \times 12)$
= 1680 : 480 : 432 = 35 : 10 : 9
B's share = Rs.$\left( {21600 \times \displaystyle\frac{{10}}{{54}}} \right)$=Rs.4000

22. Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is :
a. Rs.1500
b. Rs.1600
c. Rs.1625
d. Rs.1650

Answer: C

Explanation:
Ratio of rents = $(18 \times 4:25 \times 2:28 \times 5:21 \times 3)$ =72 : 50 : 140 : 63
Let total rent = Rs.x
Then, A's share = Rs.$\left( {x \times \displaystyle\frac{{72}}{{325}}} \right) = $ Rs.$\left( {\displaystyle\frac{{72x}}{{325}}} \right)$
$\displaystyle\frac{{72x}}{{325}} = 360$ or x = $\displaystyle\frac{{325 \times 360}}{{72}} = 1625$

23. A, B and C start a business. A Invests 3 times as much as B Invests two-third of what C Invests. Then, the ratio of capitals of A, B and C:
a. 3:9:2
b. 6:10:15
c. 5:3:2
d. 6:2:3

Answer: D

Explanation:
Suppose C invests Rs.x. Then, B invests Rs.$\left( {\displaystyle\frac{{2x}}{3}} \right)$ and A invests Rs.(2x)
Ratio of investments of A,B,C = 2x : ${\displaystyle\frac{2}{3}x}$ : 2x or 6:2:3

Alternatively:
Check the answer options where 2/3 rd of C is B and 3 times of B is A. Only D satisfies.

24. A,B,C enter into a partnership and their capitals are in the proportion of $\displaystyle\frac{1}{3}:\displaystyle\frac{1}{4}:\displaystyle\frac{1}{5}$, A withdraws half his capital at the end of 4 months. Out of total annual profit of Rs.847, A's share is :
a. Rs.252
b. Rs.280
c. Rs.315
d. Rs.412

Answer: B

Explanation:
Ratio of capitals in the beginning = ${\displaystyle\frac{1}{3}:\displaystyle\frac{1}{4}:\displaystyle\frac{1}{5}}$ = 20:15:12 ( by multiplying the ratio by 60)
Ratio of investments for the whole year = $(20 \times 4 + 10 \times 8)$ : $(15 \times 12)$ : $(12 \times 12)$ = $40:45:36$
A's share = Rs.$\left( {847 \times \displaystyle\frac{{40}}{{121}}} \right)$= Rs.280