Partnership Questions and Answers

Answer: C

They received ₹ 1,100 and ₹ 1,700.

Half the profit, ₹ 1,400, is shared equally: ₹ 700 each. The other ₹ 1,400 is shared in the ratio of capitals, \(3000 : 7500 = 2 : 5\):

\[ \begin{aligned} \text{first} &= 1400 \times \tfrac{2}{7} = 400 \\ \text{second} &= 1400 \times \tfrac{5}{7} = 1000 \end{aligned} \]

Totals: \(700 + 400 = 1100\) and \(700 + 1000 = 1700\), which add to the profit of ₹ 2,800. Every option adds to 2,800, so the sum alone does not decide it; only this split gives the right shares.

Answer: B

The ratio of the times is 15 : 12 : 10. Profit is proportional to the capital multiplied by the time, so the time is proportional to profit divided by capital.

\[ t_X : t_Y : t_Z = \frac{6}{8} : \frac{3}{5} : \frac{2}{4} \]

\[ = 0.75 : 0.6 : 0.5 = 15 : 12 : 10 \]

The options 13 : 8 : 5, 18 : 5 : 9 and 20 : 15 : 8 do not match these three values, so the second option is the answer. As a check, capitals of 8, 5 and 4 units for times of 15, 12 and 10 give products of 120, 60 and 40, which are in the ratio 6 : 3 : 2 of the profits.

Answer: D

A gets Rs. 15,400.

The ratio 7/3 : 9/4 : 12/5 becomes 140 : 135 : 144 over 60. After 6 months C raises his share by 75%, so C's investment is 144 for 6 months and 252 for the next 6 months. The shares are in proportion to investment times months: A 140 × 12 = 1680, B 135 × 12 = 1620, C 144 × 6 + 252 × 6 = 2376, a total of 5676.

\[ 52030\times\frac{1680}{5676}=15400 \]

The other amounts do not match this proportion.

Using the ratio of investment times time is the standard method for partnerships. The profit is divided in the ratio 1680 : 1620 : 2376, which simplifies to 140 : 135 : 198 and totals 473 parts. Each part is 52030 / 473 = 110, so A gets 140 × 110 = 15400.

Answer: D

The total profit is ₹ 38,000. Profit is shared in the ratio of capital times period. P's capital is 1 part for 3 units of time and Q's is 2 parts for 1 unit of time. \[ P : Q = 1\times 3 : 2\times 1 = 3 : 2 \] P's share is \(\frac{3}{5}\) of the profit, so \[ \text{Total} = 22800\times\frac{5}{3} = 38000 \] Reversing the periods would give a ratio of 1 : 6 and a very different total, and ₹ 36,000, ₹ 36,900 and ₹ 42,000 do not match P's share of 3 out of 5 parts.

Answer: A

Take the capitals as 4, 5 and 6, and the year as 12 months. A's capital changes after 8 months to half of C's initial 6, that is 3.

\[ A: 4 \times 8 + 3 \times 4 = 32 + 12 = 44 \]

\[ B: 5 \times 12 = 60 \]

\[ C: 6 \times 12 = 72 \]

\[ \text{total} = 176 \]

B's Rs. 7500 corresponds to 60 of those 176 parts:

\[ \text{total profit} = 7500 \times \frac{176}{60} = \text{Rs. } 22{,}000 \]

Answer: C

Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.

Let their initial investments be 6x, 2x and 3x respectively.

Ratio (6x * 2) + (3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 ==>7 : 8 : 6.

B’s share = 420 * 8/21 = Rs. 160.

Answer: D

Profit received by N as working partner = 14.5% of Rs. 24000 = Rs. 3480

Balance in profit = 24000 - 3480 = Rs. 20520 

Ratio of M and N =1,80,000 : 90,000 ==>2:1

Then M’s share 3 20520 2 ? Rs 13680

Answer: B

Let the total profit be \(Rs. 100.\)

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

If Rupam's share is \(Rs. 57,\) total profit \(= Rs. 100.\)

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

Answer: C

With equal periods, profits divide in the ratio of the investments.

\[ \frac{30000}{Q} = \frac{2}{3} \quad\Longrightarrow\quad Q = \text{Rs. } 45{,}000 \]

Answer: D

Profit shares are proportional to capital multiplied by time.

Take A's investment as 6 units, so B has 3 and C has 2. Let A's time be \( t \); then B's is \( 2t \) and C's is \( \tfrac{2t}{3} \).

\[ A: 6 \times t = 6t \]

\[ B: 3 \times 2t = 6t \]

\[ C: 2 \times \frac{2t}{3} = \frac{4t}{3} \]

A and B tie for the largest share, so both A and B earn the highest profit.