Fill in the blanks:

A, B, and C start a business by investing ₹40,000, ₹60,000, and ₹80,000, respectively. The total profit at the end of the year is ₹1,80,000. C’s share of the profit is ___.

₹72,000
(Total ratio = 40,000:60,000:80,000 = 4:6:8 = 2:3:4; C’s share = (4/9) × 1,80,000 = ₹72,000)

True or False:

If A and B invest in a business for the same duration, their profit share is determined solely by the amount of capital invested.

True
(Profit is proportional to the capital invested if the time period is the same)

Riddle:

A and B invest in a business. A invests ₹50,000 for 10 months, and B invests ₹75,000 for 6 months. Who gets the larger share of the profit?

A gets the larger share
(A’s contribution = 50,000 × 10 = 5,00,000; B’s contribution = 75,000 × 6 = 4,50,000; A’s contribution is higher)

 Fill in the blanks:

A, B, and C invest in a business. The profit is distributed in the ratio 5:7:8. If C’s share is ₹48,000, then the total profit is ___.

₹1,20,000
(Total ratio = 5+7+8 = 20; Total profit = 48,000 × (20/8) = ₹1,20,000)

True or False:
In a compound partnership, the share of profit depends only on the amount invested and not on the time period of investment.

False
(In a compound partnership, profit is distributed based on both investment amount and time period)

Fill in the blanks:

A and B start a business, and after 4 months, C joins. A, B, and C invest in the ratio 3:2:5. If the total profit is ₹1,00,000, C’s share is ___.

₹31,250
(C's actual ratio = 5 × 8 = 40, Total ratio = (3×12 + 2×12 + 5×8) = 36+24+40 = 100, C’s share = (40/100) × 1,00,000 = ₹31,250)

Riddle:

A, B, and C start a partnership. A’s investment is half of B’s, and B’s investment is two-thirds of C’s. If C invested ₹36,000, how much did A invest?

₹12,000
(B = (2/3) × 36,000 = 24,000; A = (1/2) × 24,000 = ₹12,000)

True or False:

A sleeping partner is one who provides capital but does not take part in business operations, yet still shares profits and losses.

True
(A sleeping partner only invests but is entitled to both profits and losses)

Fill in the blanks:

A and B start a business by investing in the ratio 4:5. After 6 months, C joins with capital equal to A. If the total profit at the end of the year is ₹1,80,000, C’s share of the profit is ___.

₹40,000
(A’s investment = 4×12 = 48, B’s investment = 5×12 = 60, C’s investment = 4×6 = 24; Total ratio = 48:60:24 = 8:10:4; C’s share = (4/22) × 1,80,000 = ₹40,000)

Fill in the blanks:

If A and B invest in a business in the ratio 5:8 and the total loss is ₹52,000, then A’s loss is ___.

₹20,000
(A’s share = (5/13) × 52,000 = ₹20,000)

Riddle:

A invests ₹30,000 for 6 months, and B invests ₹20,000 for 9 months. Who gets a greater share of profit?

A and B get an equal share
(A’s contribution = 30,000 × 6 = 1,80,000; B’s contribution = 20,000 × 9 = 1,80,000; Both contribute equally)

True or False:

In a partnership, if the partners agree to share profits unequally, the losses must also be shared unequally in the same ratio.

True
(Profit-sharing and loss-sharing must follow the same agreed ratio unless specified otherwise in the agreement)

Fill in the blanks:

A and B start a business in the ratio 2:3. After 6 months, A withdraws half of his capital. If the business runs for a year, the final ratio of their investments will be ___.

3:5
(A’s investment = 2×6 + (1/2)×2×6 = 12+6 = 18; B’s investment = 3×12 = 36; Ratio = 18:30 = 3:5)

True or False:

A partner who joins an existing partnership is entitled to a share in previous years' profits.

False
(New partners only get profit shares from the time they join)

Fill in the blanks:

A and B start a business with initial capital in the ratio 5:6. After 4 months, A withdraws half of his investment. If the business runs for a year, the final ratio of their capital will be ___.

16:21
(A’s effective capital = (5×4) + (5/2)×8 = 20+20 = 40; B’s effective capital = 6×12 = 72; Ratio = 40:72 = 16:21)