A, B and C start a business by investing ₹7,000, ₹8,000 and ₹12,000 respectively. After a year, B gets ₹3,200 as his share of profit. What is the total profit?
- (a)₹16,600
- (b)₹10,000
- (c)₹21,600
- (d)₹10,800
Correct — D, ₹10,800. All three invested for the same length of time, so profit divides in the ratio of the capitals: 7,000 : 8,000 : 12,000, which reduces to 7 : 8 : 12. The parts add to 27, and B holds 8 of them, so B's share is 8/27 of the total profit. Setting 8/27 of the profit equal to ₹3,200 gives a profit of 3,200 × 27 ÷ 8 = 400 × 27 = ₹10,800. The other two shares follow at once: A takes 7 × 400 = ₹2,800 and C takes 12 × 400 = ₹4,800, and 2,800 + 3,200 + 4,800 returns 10,800.
- (a)₹16,600 — Fits no share of the ratio. Dividing 16,600 in 7 : 8 : 12 would give B about 4,919, well above the 3,200 the question states.
- (b)₹10,000 — A rounded value that breaks the arithmetic — one part would be 10,000 ÷ 27, which is not a whole number of rupees, and B's share would come to about 2,963.
- (d)₹21,600 — Exactly twice the correct total. It is what you get by treating B's 3,200 as a share of half the profit, or by doubling the value of one part somewhere in the working.
In a simple partnership all partners contribute for the same period, and profit divides in the ratio of the amounts invested. When the periods differ the ratio is of capital multiplied by time, the so-called monthly equivalent — this is what separates a simple partnership from a compound one. A working partner's salary, where the question mentions one, comes off the profit before the remainder is divided.
The efficient route is to find the value of one part rather than to solve for the total directly. Here B's 8 parts are worth 3,200, so one part is 400, and every share and the total can be written down without further work. That habit protects against the commonest error in ratio questions, which is answering for the wrong quantity — the stem asks for the whole profit, while the ratio naturally produces individual shares.
- With equal investment periods, profit divides in the ratio of the capitals.
- 7,000 : 8,000 : 12,000 reduces to 7 : 8 : 12, a total of 27 parts.
- B's 8 parts equal ₹3,200, so one part is ₹400.
- The total profit is 27 × 400 = ₹10,800, with A on ₹2,800 and C on ₹4,800.
- When periods differ, use capital multiplied by time to build the ratio.
Finding the value of one part turns every remaining question into a multiplication.
- Reporting B's share, or the sum of A and C's shares, instead of the total profit.
- Failing to reduce the capitals to their simplest ratio before counting parts.
- Using capital-times-time when all the investments ran for the same period, which changes nothing but invites arithmetic slips.
A one-step partnership item. The whole question is the value of a single part.
The cost of gold varies directly as the cube of its weight. A gold piece weighing 20 decigram costs ₹1,000. If it is broken into two pieces whose weights are in the ratio 2 : 3, then what is the profit or loss incurred?
- (a) ₹280 profit
- (b) ₹280 loss
- (c) ₹720 profit
- (d) ₹720 loss
Answer(d) ₹720 loss
Splitting a quantity in a given ratio, with one extra step. There the ratio divides the weight and a cube law then converts each piece into money, where here the ratio divides the profit directly.
- practice — not a real PYQ
A and B invest ₹5,000 and ₹7,000 for the same period. If the total profit is ₹4,800, B's share is
- (a)₹2,000
- (b)₹2,400
- (c)₹2,800
- (d)₹3,000
Answer(c) ₹2,800 — the ratio 5 : 7 has 12 parts, so one part is 400 and B takes 7 of them.
- practice — not a real PYQ
A invests ₹6,000 for 12 months and B ₹9,000 for 8 months. Their profits divide in the ratio
- (a)2 : 3
- (b)1 : 1
- (c)3 : 2
- (d)4 : 3
Answer(b) 1 : 1 — capital times time gives 72,000 each.