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Partnership Exercise 2

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  1. Question 1 of 14
    1. Question

    Three men A, B and C together subscribe Rs 4700 for a business. A puts in Rs 700 more than B and B puts in Rs 500 more than C. How much B will receive out of a total profit of Rs 4230?

    Hint

    If C puts in Rs x, then B puts in Rs x + 500 and A puts in (x +500)

    + 700 i.e. x + 1200

    ⇒ (x + 1200) + (x + 500) + x = 4700

    ⇒ 3x + 1700 = 4700

    ⇒ x = 1000

    Ratio of their investment 2200 : 1500 : 1000 = 22 : 15 : 10

    Thus, share of

    partnership-q-49852.png

  2. Question 2 of 14
    2. Question

    A and B are partners in a business. A contributes ¼ of the capital for 15 months and B received ⅔ of the profit. For how long B’s money was used?

    Hint

    Let the total profit be Rs z. Then,

    B’s share = Rs partnership-q-49846.png

    A’s share = Rs partnership-q-49840.png

    partnership-q-49834.png

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

    partnership-q-49828.png

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

  3. Question 3 of 14
    3. Question

    In a partnership between A, B and C, A’s capital is Rs 4,000. If in a profit of Rs 800. A’s share is Rs 200 and C’s share is Rs 100, then B’s capital is

    Hint

    Let B’s capital is x and c’s capital is y.

    ∴ A’s profit

    = 200partnership-q-49822.png …(i)

    and C’s profit

    = 100 partnership-q-49816.png … (ii)

    Equation (i) ÷ Equation (ii)

    ⇒partnership-q-49810.png

    ∴ x = Rs 10,000

  4. Question 4 of 14
    4. Question

    A began business with Rs 12500 and is joined afterwards by B with Rs 37500. When did B join, if the profits at the end of the year are divided equally?

    Hint

    Let B join after x months of the start of the business so that B’s money is invested for (12–x) months.

    ∴ Profit ratio is 12 × 12500 : (12 – x) × 37500

    ⇒ 12 : 3(12 – x)

    Since profit is equally divided. therefore

    12 = 3(12 – x)

    ⇒9 x = 8.

    Thus B joined after 8 months.

  5. Question 5 of 14
    5. Question

    A began business with Rs 45,000 and was later joined by B with Rs 54,000. When did B join if the profit at the end of the year were divided in the ratio 2 : 1?

    Hint

    Let B join after ‘x’ month of the start of the business.

    ⇒ (45,000 × 12) : 54,000 × (12 – x)

    = 2 : 1

    ∴ (45,000 × 12) × 1

    = 54,000 × (12 – x) × 2

    ⇒ x = 7

    Thus B joined after 7 months.

  6. Question 6 of 14
    6. Question

    A and B rent a pasture for 10 months; A puts in 80 cows for 7 months. In how many cows can B put for the remaining 3 months, if he pays half as much again as A?

    Hint

    Let B puts in x cows

    Then amount paid by

    partnership-q-49803.png.

    partnership-q-49797.png

    partnership-q-49791.png

    partnership-q-49785.png

    partnership-q-49779.png

    Hence, B puts in 280 cows

  7. Question 7 of 14
    7. Question

    Two friends P and Q started a business investing in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q’s. At the end of the year, 20% profit was earned which was equal to Rs 98,000. What was the amount invested by R?

    Hint

    Let the total investment be Rs x.

    Then, 20% of x = 98000

    partnership-q-49773.png

    Let the capitals of P, Q and R be Rs 5x, Rs 6x and Rs 6x respectively. Then,

    (5x × 12) + (6x × 12) + (6x × 6) = 490000 × 12

    partnership-q-49767.png

    ∴ R’s investment

    = 6x = Rs (6 × 35000) = Rs 210000.

  8. Question 8 of 14
    8. Question

    In a partnership, A invests ⅙ of the capital for ⅙ of the time, B invests ⅓ of the capital for ⅓ of the time and C, the rest of the capital for whole time. Find A’s share of the total profit of Rs 2,300.

    Hint

    Remaining capital

    partnership-q-49761.png

    Ratio of their profit

    partnership-q-49755.png

    partnership-q-49749.png

    ∴ A’s share

    = partnership-q-49743.png

  9. Question 9 of 14
    9. Question

    A, B and C start a business each investing Rs 20,000. After 5 months A withdrew Rs.5000, B withdrew Rs 4000 and C invests Rs 6000 more. At the end of the year, a total profit of Rs 69,900 was recorded. Find the share of B.

    Hint

    Ratio of the capitals of A, B and C

    = 20000 ×5 + 15000 × 7 : 20000 × 5 + 16000 × 7 : 20000 × 5 + 26000 × 7

    = 205000 : 212000 : 282000

    = 205 : 212 : 282.

    B’s share = Rspartnership-q-49736.png

    = Rs 21,200

  10. Question 10 of 14
    10. Question

    A is a working partner and B is a sleeping partner in a business. A puts in Rs 50,000 and B Rs 60,000. A gets 12.5% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of A in profit of Rs 8800.

    Hint

    The amount A gets for managing the business

    = 12.5% of Rs 8800

    = Rs 1100

    Remaining profit

    = Rs 8800 – Rs 1100

    = Rs 7700

    This is to be divided in the ratio 5 : 6.

    A’s share

    partnership-q-49730.png

    = Rs 3500

    ⇒ Total share of A

    = Rs 3500 + Rs 1100

    = Rs 4600.

  11. Question 11 of 14
    11. Question

    A and B invest Rs 3,000 and Rs 4,000 in a business respectively. A receives Rs 10 per month out of the profit as a remuneration for running the business and the rest of profit is divided in proportion to the investments. If in a year ‘A’ totally receives Rs 390, what does B receive?

    Hint

    In a year, for A, total amount as a remuneration

    = 10 ×12 = Rs 120

    ∴ Amount of A’s profit

    = 390 – 120 = Rs 270

    Ratio of investment = 3 : 4

    Let total profit be Rs x

    Then, B’s profit = Rs(x – 270)

    ∴ A’s share

    = partnership-q-49723.png

    ∴ B’s profit = 630 – 270 = Rs 360

  12. Question 12 of 14
    12. Question

    A and B entered into a partnership with capitals in the ratio of 4 : 5. CDATA[ After 3 months, A withdrew ¼ of his capital and B withdrew ⅕ of his capital. The gain at the end of 10 months was Rs 760. Find the profit of B.

    Hint

    Let A’s capital be Rs 4x and B’s capital be Rs 5x

    ∴ Ratio of profit

    = 4x × 3 + partnership-q-49717.png: partnership-q-49711.png

    = 33 : 43

    ∴ Profit of B partnership-q-49705.png

    = Rs 430

  13. Question 13 of 14
    13. Question

    In a partnership between X and Y, X’s capital is ⅖ of total and is invested for ⅔ year. If his share of the profit is ⁴⁄₇ of the total, for how long is Y’s capital in the business?

    Hint

    Since, x’s capital

    partnership-q-49699.png

    ∴ y’s capital

    partnership-q-49693.png

    Let y invested capital for t years.

    ∴ partnership-q-49687.png

    partnership-q-49681.png … (i)

    Share of y’s profit

    partnership-q-49674.png of the total

    Actual ratio of profit = 4 : 3

    ∴ By (i), partnership-q-49668.png

    partnership-q-49662.png

  14. Question 14 of 14
    14. Question

    X and Y put in Rs 3,000 and Rs 4,000 respectively into a business. X reinvests into the business his share of the first year’s profit of Rs 2,100 whereas Y does not reinvest. In what ratio should they share the second year’s profit?

    Hint

    For first year, ratio of profit = 3 : 4

    X’s profit of first year

    partnership-q-49656.png

    Now, for second year, Ratio of profit

    = 3000 × 12 + 900 × 12 : 4000 × 12

    = 46800 : 48000

    = 39 : 40

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