Question: 6 -

Raju started a business with Rs. 900. Kamal joined him after few months with an amount of 600. If the profits at the end of the year were divided in the ratio of 2:1, after how many months Kamal joined the business?

9 months

5 months

3 months

8 months

Answer:

3 months

Solution:

The capital of Raju (C1) =900
And the capital of Kamal is (C2) = 600

Time period spend by Raju (T1) = 12 months
Let the time period spend by Kamal (T2) = x months

The ratio of their profit (p1:p2) is 2: 1

Apply the formula:
(C1 * T1)/ (C2 * T2) = p1/p2
(900 * 12)/ (600*x) = (2/1)
10800/600 = 2* x
x= 18/2
x= 9 months, i.e., Kamal spend 9 months.
So, Kamal joined after, 12 - 9= 3 months.

Question: 7 -

Mahesh and Suresh rent a pasture for 12 months. Mahesh puts in 200 cows for 8 months. How many cows can Suresh put in the pasture for the remaining 4 months if he pays 1(1/2) as much as Mahesh?

300 cows

520 cows

600 cows

450 cows

Answer:

600 cows

Solution:

Let Mahesh's cow (C1) = 200 cows, and time spend T1 = 8 months
Suresh's cow (C2) = y cows, and time spend T2 = 4 months
Let the profit of Mahesh = x
Then the profit of Suresh = 1(1/2)*x

Apply profit ratio formula:

(C1 * T1)/ (C2 * T2) = p1/p2
(200 * 8)/ (y*4) = (x/ (3x/2))
400/y = 2x/3x
400/y = 2/3
y = (400*3)/2
y= 600

Hence, Suresh can put 600 cows for the remaining 4 months.

Question: 8 -

Ramesh and Suresh enter into a partnership with capitals in the ratio of 10:12. At the end of 8 months, Ramesh withdraws. If they receive profits in the ratio of 10:18. Find how long Suresh's capital was used.

7 months

12 months

8 months

10 months

Answer:

12 months

Solution:

Let the capital of Ramesh (C1) =10
And the capital of Suresh is (C2) = 12

Time period spend by Ramesh (T1) = 8 months
Let, time period spend by Suresh (T2) = x months

The ratio of their profit (p1:p2) is 10: 18
Apply formula: (C1 * T1)/ (C2 * T2) = p1/p2
(10 * 8)/ (12*x) = (10/18)
(80/12x) = (5/9)
20/3x = 5/9
180 = 15x
Hence, x=12 months

Question: 9 -

Praveen and Sunny enter into a partnership. Praveen puts in Rs. 50 and Sunny put in Rs. 45. At the end of 4 months Praveen withdraws half of his capital, and at the end of 6 months, Sunny withdraws half of his capital. Ashu Bhati then enters with a capital of Rs. 70. At the end of 12 months, in what ratio will the profit be divided?

65:32:56

84:82:80

54:60:66

80:81:84

Answer:

80:81:84

Solution:

Let Praveen's capital is C1 = 50 for period T1= 4 months, and C11= 25 for period T11= 8
Sunny's capital is C2 = 45 for period T2 = 6 months, and C22 = 45/2 for period T22= 6 months.
Ashu Bhati's capital is C3 = 70 for period T3 = 6 months.

Now, apply the profit ratio formula:

(C1 * T1): (C2 * T2): (C3 * T3) = p1: p2: p3
But here we have 2 different values for Praveen and Sunny.
So, (C1 * T1 + C11 * T11): (C2 * T2 + C22 * T22): (C3 * T3) = p1: p2: p3
Now, (50*4 + 25*8): (45*6 + (45*2)/6): (70*6) = p1: p2: p3
The ratio of their profit is p1: p2: p3 = 400: 405: 420
Divide all ratios by 25.
Hence, the ratio will be 80: 81: 84

Question: 10 -

X and Y enter into a partnership for a year. X invests Rs. 6000, and Y invests Rs. 8000. After 4 months, they admit Z, who invests Rs. 9000. If Y withdraws his contribution after 6 months, how would they share a profit of Rs 1000 at the end of the year?

350, 300, 350

375, 250, 375

100, 600,300

400, 300, 300

Answer:

375, 250, 375

Solution:

X's capital be C1 = 6000
Y's capital be C2 = 8000
Z's capital be C3 = 9000
X's time be T1 = 12 months
Y's time be T2 = 6 months
Z's time be T3 = 8 months
Profit = 1000

The profit will be divided in the ratio:-

(C1 * T1): (C2 * T2): (C3 * T3)
(6000*12): (8000*6): (9000*8)
i.e., 72000: 48000: 72000
Or, 72:48:72
Divide the whole equation by 24.
The ratio will be 3: 2: 3
Sum of the ratios will be 3+2+3= 8

Apply formula:

X's share = (X's ratio/ sum of all three ratios)* total profit
Hence, X's share is (3/8) * 10000 = 375
X's and Z's share are equal in ratio, so Z's share =375
Y's share = 1000 - (A + B)'s share
= 1000 - 750 = 250