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21. Two partnets invest Rs 125,000 and Rs 85,000 respectively in a venture and agreed that 60% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs 300 more than the other, find the total profit made in the business.
  A.  Rs 3754.50
  B.  Rs 4137.10
  C.  Rs 3937.50
  D.  Rs 38350.50
     
   
View Answer

Shortcut:
Two partners invest Rs m and Rs n respectively in a business and agree that Q% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner get Rs Z more than the other then to find the total profit made in the business we adopt the following steps.
Step 1.
First find the ratio of the profit Rs m : Rs n = A:B (say)
Step 2.
Now, apply the following formula to calculate the total profit.
Total profit= Rs Z
(
100 / 100-Q
)
(
A+B / A-B
)

Here,
Step 1.
ratio of profit = 125000:85000 = 25 : 17
Step 2.
Total profit= Rs 300
(
100 / 100-60
)
(
25+17 / 25-17
)
= Rs 3937.50

22. Amit and Babbi invested in the ratio 3 : 2 in a business. If 5% of the total profit goes to charity and Amit's share is Rs 855, find the total profit.
  A.  Rs 2100
  B.  Rs 1900
  C.  Rs 1300
  D.  Rs 1500
     
   
View Answer

Shortcut:
Two partners M and N invests in the ratio a:b in a business. If Q% of the total profit goes to charity and M's share is Rs Z, then the toal profit is given by Rs Z
(
100 / 100-Q
)
(
1+
b / a
)

Here, Z=855 Q= 5, a = 3 and b=2
Putting these values in the shortcut, we get
Rs 855
(
100 / 100-5
)
(
1+
2 / 3
)

Rs 855
(
100 / 95
)
(
1+
5 / 3
)
= Rs 1500

23. Three partners invested Rs 114,000 in a business. At the end of the year, one got Rs 337.50, the second Rs 1125.00 and the third Rs 675 as profit. How much amount did each invest? What is the percentage of profit?
  A.  1.857%
  B.  2.5%
  C.  5%
  D.  3.857%
     
   
View Answer

Shortcut:
The ratio of investments = Ratio of profits = 337.50 : 1125 : 675 = 3375 :11250 : 6750
Dividing eabh by 1125, we have the ratio 3:10:6
Shares of the partners = Rs
114000 / 3+10+6
x3,
114000 / 3+10+6
x10, and Rs
114000 / 3+10+6
x6
or, Rs 18000, Rs 60000 and Rs 36000
The required percentage of profit =
337.5 + 1125 + 675 / 114000
x100 =
2137.50 / 1140
= 1.857%

24. A, B and C started a shop by investing Rs 2700, Rs 8100 and Rs 7200 respectively. At the end of one yer, the profit was distributed . If B's share ws Rs 3600, their total profit was.
  A.  Rs 2000
  B.  Rs 8000
  C.  Rs 6000
  D.  Rs 3000
     
   
View Answer

Ratio of shares of A, B and C= 2700 : 8100 : 7200 = 3 : 9 : 8
If B's share is Rs 9, total profit = Rs 20
If Ram's shares is Rs 3600, total profit =
20 / 9
x 3600 = Rs 8000

25. Amit puts Rs 600 more in a business than Bhim, but Bhim has invested his capital for 5 months while Amit has invested his for 4 months. If the sharte of Amit is Rs 48 more than that of Bhim out of the total profit of Rs 528, find the capital contributed by each?
  A.  Amit's capital: Rs 1300; Bhim's capital:Rs 1700
  B.  Amit's capital: Rs 900; Bhim's capital:Rs 2100
  C.  Amit's capital: Rs 1650; Bhim's capital:Rs 1350
  D.  Amit's capital: Rs 1800; Bhim's capital:Rs 1200
     
   
View Answer

Shortcut: Two partners A and B start a business. A puts in Rs 'A' more in the business than B, but B has invested his capital for T2 periods while A has invested his capital for T1 periods. If the share of A is Rs 'a' more than that of B out of the total profits of Rs 'Z', then the capital contributed by B is
[
A /
(Z+a)T2 / (Z-a)T1
- 1
]
and the capital contributed by A is given by [Rs A + capital of B]
Here,
A = 600, Z=528, a=48, T1=4, T2 = 5
using these values in shortcut, we get:
[
600 /
(528+48)5 / (528-48)4
- 1
]
=
[
600 /
576 x 5 / 480 x 4
- 1
]
=
[
600 /
3 / 2
- 1
]
= Rs 1200 A's capital = Rs 1200 + Rs 600 = Rs 1800

26. Amit, Bhim and Chinto can do a work in 20, 25 and 30 days respectively. they undertook to finish the work together for Rs 2220, then the share of Amit exceeds that of Bhim by
  A.  Rs 180
  B.  Rs 150
  C.  Rs 200
  D.  Rs 170
     
   
View Answer

Ratio of shares = Ratio of 1 day's work =
1 / 20
:
1 / 25
:
1 / 30
= 15 : 12 : 10
∴ Amit's share = Rs 2220 x
15 / 37
= Rs 900
Bhim's share = 2220 x
12 / 37
= Rs 720
Hence, Amit's share exceeds Bhim's shares by Rs (900 - 720) = Rs 180

27. A, B and C enter into partnership by making investments in the ratio 3 : 5 : 7. After a year, C invests another Rs 337600 while A withdraws Rs 45600. The ratio of investments then changes to 24 : 59 : 167. How much did A invest initially?
  A.  Rs 1,20,300
  B.  Rs 2,61,100
  C.  Rs 1,41,600
  D.  Rs 3,77,900
     
   
View Answer

Let the initial investments of A,B and C be Rs 3y, Rs 5y and Rs 7y respectively.
Then, (3y - 45600) : 5y : (7y + 337600) = 24 : 59 : 167
∴
3y - 45600 / 5y
=
24 / 59

⇒ y = 47200
∴ A invested initially Rs (47200 x 3) = Rs 141600

28. A sum of money is to be divided among A, B and C in the ratio 2 : 3 : 7. If the total share of A and B together is Rs 1500 less than C, what is A's share in it?
  A.  Rs 1300
  B.  Rs 1500
  C.  Rs 1700
  D.  Rs 2000
     
   
View Answer

7x - (2x + 3x) = Rs 1500
∴ x = Rs 750
∴ A = 2x = Rs 750 x 2 = Rs 1500

29. A and B invest Rs 3000 and Rs 4000 in a business. A receives Rs 10 per month out of the profit as remuneration for running the businss and the rest of profitis divided in proportion to the investments. If in a year A total receives Rs 390, what does B receive?
  A.  Rs 290
  B.  Rs 310
  C.  Rs 430
  D.  Rs 360
     
   
View Answer

Total profit - remuneration = Balance profit.
This balance profit is divided in proportion to their investments
Balance profit of A / Balance profit of B
=
Investment of A / Investment of B

or,
390 - 10 x 12 / Balance profit of B
=
3000 / 4000
=
3 / 4
(since remuneration of A is Rs 10 per month)
or, Balance profit of B = 4 x
270 / 3
= Rs 360
Since B does not get any remubneration, hence B recieves Rs 360 at the end of the year.

30. A, B and C got a work for Rs 550. Together A and B are to do
7 / 11
of the work. The share of C should be.
  A.  Rs 400
  B.  Rs 150
  C.  Rs 200
  D.  Rs 330
     
   
View Answer

A and B do
7 / 11
work out of total.
Remaining work for C to do = 1 -
7 / 11
=
11 - 4 / 11
=
4 / 11

The share of C =
4 / 11
x 550 = 4 x 50 = Rs 200

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