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