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. |

- 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?
- \(Rs.10,000\)
- \(Rs.20,000\)
- \(Rs.30,000\)
- \(Rs.40,000\)

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, $$ = \frac{2}{5} \times 25,000 $$ $$ = Rs.10,000 $$

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, $$ = \frac{2}{5} \times 25,000 $$ $$ = Rs.10,000 $$

- 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?
- \(3 \ months\)
- \(6 \ months\)
- \(9 \ months\)
- \(12 \ months\)

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

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

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

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

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

- 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?
- \(Rs.2565.3\)
- \(Rs.2666.6\)
- \(Rs.2858.5\)
- \(Rs.2828.6\)

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, $$ 24000 : 6M = 3 : 2 $$ $$ \frac{24000}{6M} = \frac{3}{2} $$ $$ M = Rs.2666.6 $$

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, $$ 24000 : 6M = 3 : 2 $$ $$ \frac{24000}{6M} = \frac{3}{2} $$ $$ M = Rs.2666.6 $$

- 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 \(Rs.20,000\)?
- \(Rs.5678.3\)
- \(Rs.6766.6\)
- \(Rs.7652.3\)
- \(Rs.8333.3\)

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 $$ = \frac{5}{12} \times 20,000 $$ $$ = Rs.8333.3 $$

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

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

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

- 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?
- \(15.5 \ years\)
- \(17.5 \ years\)
- \(18.5 \ years\)
- \(20.5 \ years\)

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 = \(7k\) = \(17.5 \ years\)

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 = \(7k\) = \(17.5 \ years\)

- 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?
- \(4 : 5\)
- \(5 : 6\)
- \(9 : 7\)
- \(5 : 9\)

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

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

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

- 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?
- \(2.5 \ months\)
- \(3.5 \ months\)
- \(4.5 \ months\)
- \(5.5 \ months\)

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

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

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

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

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

- 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?
- \(Rs.1000\)
- \(Rs.2000\)
- \(Rs.3000\)
- \(Rs.4000\)

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 $$ = \frac{1000}{2} \times 4 $$ $$ = Rs.2000 $$

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 $$ = \frac{1000}{2} \times 4 $$ $$ = Rs.2000 $$

- 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 \(x : y : z\)?
- \(2 : 3 : 5\)
- \(3 : 5 : 7\)
- \(3 : 8 : 10\)
- \(5 : 9 : 10\)

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), $$ x : y : z = 3 : 8 : 10 $$

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), $$ x : y : z = 3 : 8 : 10 $$

- If \(5x = 3y = 7z\), then find the value of \(x : y : z\)?
- \(21 : 35 : 15\)
- \(15 : 21 : 30\)
- \(21 : 25 : 15\)
- \(20 : 22 : 25\)

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), $$ x : y : z = 21 : 35 : 15 $$

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), $$ x : y : z = 21 : 35 : 15 $$

Lec 1: Introduction
Exercise-1
Lec 2: Rules of Componendo and Dividendo
Exercise-2
Lec 3: Rules of Partnership
Exercise-3
Exercise-4
Exercise-5