# Partnership Questions

Q:

A, B, C started a business with their investments in the ratio 1:3 :5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is :

 A) 1 : 2 : 3 B) 3 : 4 : 15 C) 3 : 5 : 10 D) 5 : 6 : 10

Explanation:

Let their initial investments be x, 3x and 5x respectively. Then,

$\inline \fn_jvn A:B:C=(x\times 4+2x\times 8):(3x\times 4+\frac{3x}{2}\times 8):(5x\times 4+\frac{5x}{2}\times 8)$

20x : 24x : 40x = 5 : 6 : 10

50 11110
Q:

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) 500 B) 1000 C) 1500 D) 2000

Explanation:

Let the total profit be Rs. 100.

After paying to charity, A's share  = $\inline (95\times \frac{3}{5})$ = Rs. 57.

If A's share is Rs. 57, total profit = Rs. 100.

If A's share is Rs. 855, total profit  = $\inline (\frac{100}{57}\times 855)$ = 1500.

33 9151
Q:

A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used ?

 A) 3 months B) 6 months C) 10 months D) 12 months

Explanation:

Let the total profit be Rs. z. Then,

B's share = Rs. 2z/3,  A's share = Rs. ( z - 2z/3 ) = Rs. z/3.

A : B = z/3 : 2z/3 = 1:2

Let the total capital be Rs, X and suppose B's money was used for x months. Then.

(1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3) = 10 .

Thus, B's money was used for 10 months.

31 8084
Q:

A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?

 A) 4 months B) 5 months C) 6 months D) 8 months

Explanation:

Suppose B joined for x months . Then,  ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.

So, B joined for 8 months.

27 5047
Q:

Two partners investede Rs. 1250 and Rs. 850 respectively in a business. They distributed 60% of the profit equally and decide to distribute the remaining 40% as the ratio of their capitals. If one partner received Rs. 30 more than the other, find the total profit?

Let the total profit be Rs.x

60% of the profit = $\inline&space;\frac{60}{100}\times&space;x=Rs.\frac{3x}{5}$

from  this part of the profit each gets = Rs.$\inline&space;\frac{3x}{10}$

40% of the profit = $\inline&space;\frac{40}{100}\times&space;x=Rs.\frac{2x}{5}$

Now, this amount of Rs.$\inline&space;\frac{2x}{5}$ has been divided in the ratio of capitals 1250 : 850 = 25 :17

$\inline&space;\therefore$ Share on first capital = $\inline&space;(\frac{2x}{5}\times&space;\frac{25}{42})=Rs.\frac{5x}{21}$

Share on second capital = $\inline&space;(\frac{2x}{5}\times&space;\frac{17}{42})=Rs.\frac{17x}{105}$

Total money received by 1st investor = $\inline&space;[\frac{3x}{10}+\frac{5x}{21}]=&space;Rs.\frac{113x}{210}$

Total money received by 2nd investor = $\inline&space;[\frac{113x}{210}+\frac{97x}{210}]=Rs.\frac{97x}{210}$

$\inline&space;\therefore$ x = 393.75

Hence total profit = Rs. 393.75