## Results

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### #1. 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?

Solution:

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now,

14x/8y=5/798x=40y
y=49x/20
And, 14x/7z=5/8
112x=35z
z=112x/35=16x/5
So
x:y:z=x:49x/20:16/x5
(Multiply by 20)20:49:64

### #2. Three partners A , B , C start a business . B’s Capital is four times C’s capital and twice A’s capital is equal to thrice B’s capital . If the total profit is Rs 16500 at the end of a year ,Find out B’s share in it.

Solution:

Suppose C’s capital = x then
B’s capital = 4x (Since B’s Capital is four times C’s capital)
A’s capital = 6x ( Since twice A’s capital is equal to thrice B’s capital)
A : B : C =6x : 4x : x
= 6 : 4 : 1
B’s share = 16500×4/11 = 1500 × 4 = 6000.

### #3. Kamal started a business investing Rs 9000. After five months, Sameer joined with a capital of Rs 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit ?

Solution:

Now as per question, Kamal invested for 12 months and Sameer invested for 7 months.
So Kamal : Sameer = (9000 × 12) : (8000 × 7)
= 108 : 56
= 27 : 14
Sameer Ratio in profit will be

=(6970×14/41)=Rs. 2380

### #4. P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is

Solution:

Let the amount invested by Q = q.

40000:q=2:3
40000q=2/3
q=40000×3/2
=Rs. 60000

### #5. If 4 (P’s Capital ) = 6 ( Q’s Capital ) = 10 ( R’s Capital ) , then out of the total profit of Rs 4650 , R will receive

Solution:

Let
P’s capital = p,
Q’s capital = q and
R’s capital = r.
Then

4p=6q=10r
2p=3q=5r
q=2p/3
r=2p/5
P:Q:R
=p:2p/3:2p/5
(Multiply by 15)
=15:10:6
R’s share
=4650×6/31
=150×6
=Rs900

### #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?

Solution:
A:B:C
=(10×7):(12×5):(15×3)=
70:60:45
=14:12:9
C’s rent
=Rs.(175×9/35)
=Rs45

### #7. 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?

Solution:

Assume that investment of C = x
Then, investment of A = 2x
Investment of B = 2A/3 = 4x/3
(since ratio of investment of A : B = 2 : 3 i.e B = 2A/3)
A : B : C= 2x : 4x/3 : x
= 2 : 4/3 : 1
= 6 : 4 : 3

B’s Share
=157300×4/6 4 3
=157300×4/13
=12100×4
=Rs. 48400

### #8. 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?

Solution:

A : B : C
= (20,000 × 24) : (15,000 × 24) : (20,000 × 18)
= 4 : 3 : 3.

So B’s Share=Rs25000×3/10=Rs. 7500

### #9. P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs . In what ratio should the profit be divided at the end of 3 years?

Solution:

P : Q : R
= (25 × 1 35 × 2) : (35 × 2 : 25 × 1) : (30 × 3)
= 95 : 95 : 90
= 19 : 19: 18