Ratio and Proportion Aptitude Questions and Answers:


Overview:


Questions and Answers Type:MCQ (Multiple Choice Questions).
Main Topic:Quantitative Aptitude.
Quantitative Aptitude Sub-topic:Ratio and Proportion Aptitude Questions and Answers.
Number of Questions:10 Questions with Solutions.

  1. Rohit and Mohit investing \(Rs.20,000\) and \(Rs.30,000\) respectively into partnership, and both agree to share the profit in the ratio of their capitals. Find the share of Rohit in a profit of \(Rs.25,000\) after one year?

    1. \(Rs.10,000\)
    2. \(Rs.20,000\)
    3. \(Rs.30,000\)
    4. \(Rs.40,000\)


Answer: (a) \(Rs.10,000\)

Solution: Given, \(k_1 = Rs.20,000\)

\(k_2 = Rs.30,000\)

Profit = \(Rs.25,000\), then $$ k_1 : k_2 = 20,000 : 30,000 $$ $$ = 2 : 3 $$ Hence, the share of Rohit will be, $$ = \frac{2}{5} \times 25,000 $$ $$ = Rs.10,000 $$

  1. x and y started a business with the initial investments in the ratio of \(3 : 4\). If after one year their profits were in the ratio of \(1 : 2\) and the period of investment of x is six months, then find the period of investment of y?

    1. \(3 \ months\)
    2. \(6 \ months\)
    3. \(9 \ months\)
    4. \(12 \ months\)


Answer: (c) \(9 \ months\)

Solution: Let ratio of investment of x and y = \(3k : 4k\)

and period of investment of y = P, then $$ \frac{3k \times 6}{4k \times P} = \frac{1}{2} $$ $$ P = 9 \ months $$

  1. x starts a business with the initial invesment of \(Rs.2000\). y and z join the same business after \(6\) and \(9\) months respectively. If at the end of one year, the profit is divided in the ratio of \(3 : 2 : 4\) respectively, then find the invesment of y?

    1. \(Rs.2565.3\)
    2. \(Rs.2666.6\)
    3. \(Rs.2858.5\)
    4. \(Rs.2828.6\)


Answer: (b) \(Rs.2666.6\)

Solution: Let investment capital of y and z = \(M \ and \ N\)

and investment ratio of x, y, and z $$ = (2000 \times 12) : 6M : 3N $$ then the profit ratio of x, y and z $$ 24000 : 6M : 3N = 3 : 2 : 4 $$ on taking first and second term, $$ 24000 : 6M = 3 : 2 $$ $$ \frac{24000}{6M} = \frac{3}{2} $$ $$ M = Rs.2666.6 $$

  1. Three friends x, y and z, started a business and after one year the profit were in the ratio of \(3 : 4 : 5\) respectively. Find the share of z out of the profit of \(Rs.20,000\)?

    1. \(Rs.5678.3\)
    2. \(Rs.6766.6\)
    3. \(Rs.7652.3\)
    4. \(Rs.8333.3\)


Answer: (d) \(Rs.8333.3\)

Solution: profit ratio of x, y and z = \(3 : 4 : 5\)

profit amount = \(Rs.20,000\)

Hence, share of z $$ = \frac{5}{12} \times 20,000 $$ $$ = Rs.8333.3 $$

  1. The ratio of present ages of x and y is \(5 : 7\). If after five yearstheir ratio will become \(7 : 9\), then find the present age of y?

    1. \(15.5 \ years\)
    2. \(17.5 \ years\)
    3. \(18.5 \ years\)
    4. \(20.5 \ years\)


Answer: (b) \(17.5 \ years\)

Solution: Let present ages = \(5k : 7k\)

then after five years, $$ \frac{5k + 5}{7k + 5} = \frac{7}{9} $$ $$ k = 2.5 $$ Hence, the present age of y = \(7k\) = \(17.5 \ years\)

  1. Two friends started a business with the initial investments of \(Rs.5000\) and \(Rs.6000\) respectively. If they invested for two and three years respectively, then find the profit ratio of the partners?

    1. \(4 : 5\)
    2. \(5 : 6\)
    3. \(9 : 7\)
    4. \(5 : 9\)


Answer: (d) \(5 : 9\)

Solution: profit ratio will be $$ = A_1 \ T_1 : A_2 \ T_2 $$ $$ = 5000 \times 2 : 6000 \times 3 $$ $$ = 10000 : 18000 $$ $$ = 5 : 9 $$

  1. Two friends M and N started a business with the initial investments in the ratio of \(5 : 4\). If after one year profits were in the ratio of \(3 : 2\) and investment period of M was \(3\) months, then find the investment period of N?

    1. \(2.5 \ months\)
    2. \(3.5 \ months\)
    3. \(4.5 \ months\)
    4. \(5.5 \ months\)


Answer: (a) \(2.5 \ months\)

Solution: Let ratio of investment of M and N = \(5k : 4k\)

and period of investment of N = P, then $$ \frac{5k \times 3}{4k \times P} = \frac{3}{2} $$ $$ P = 2.5 \ months $$

  1. The ratio of investments of A and B is \(2 : 3\) and ratio of investments of B and C is \(3 : 4\). If A invested \(Rs.1000\), then find the investment amount of C?

    1. \(Rs.1000\)
    2. \(Rs.2000\)
    3. \(Rs.3000\)
    4. \(Rs.4000\)


Answer: (b) \(Rs.2000\)

Solution: ratio of A and B = \(2 : 3\)

ratio of B and C = \(3 : 4\)

investment amount of A = \(Rs.1000\)

since B is common then, $$ A : B : C = 2 : 3 : 4 $$ Hence, investment amount of C $$ = \frac{1000}{2} \times 4 $$ $$ = Rs.2000 $$

  1. Three partners x, y and z, invested in a business, the investmesnt ratio of x and y is \(3 : 8\) and the investment ratio of y and z is \(4 : 5\). Find the ratio of \(x : y : z\)?

    1. \(2 : 3 : 5\)
    2. \(3 : 5 : 7\)
    3. \(3 : 8 : 10\)
    4. \(5 : 9 : 10\)


Answer: (c) \(3 : 8 : 10\)

Solution: Given, $$ x : y = 3 : 8.....(1) $$ $$ y : z = 4 : 5.....(2) $$ to make the value of y equal multiply with equation (2) by \(2\), $$ y : z = 8 : 10.....(3) $$ now from the equations (1) and (3), $$ x : y : z = 3 : 8 : 10 $$

  1. If \(5x = 3y = 7z\), then find the value of \(x : y : z\)?

    1. \(21 : 35 : 15\)
    2. \(15 : 21 : 30\)
    3. \(21 : 25 : 15\)
    4. \(20 : 22 : 25\)


Answer: (a) \(21 : 35 : 15\)

Solution: from the given values,, $$ x : y = 3 : 5.....(1) $$ $$ y : z = 7 : 3.....(2) $$ to make the value of y equal multiply with equation (1) by \(7\) and with equation (2) by \(5\), $$ x : y = 21 : 35.....(3) $$ $$ y : z = 35 : 15.....(4) $$ now from the equations (3) and (4), $$ x : y : z = 21 : 35 : 15 $$