Ratio - Aptitude MCQ Questions and Solutions with Explanations

81

If x runs scored by A, y runs by B and z runs by C, then x : y = y : z = 3 : 2. If total number of runs scored by A, B and C is 342, the runs scored by each would be respectively = ?

A) 144, 96, 64 B) 162, 108, 72 C) 180, 120, 80 D) 189, 126, 84

Discuss

Answer & Solution

Answer: Option B

Solution:

Given,
X : Y = 3 : 2
Y : Z = 3 : 2
Equal the value of Y in both equation
X : Y = 3 : 2 (multiply with 3) and
Y : Z = 3 : 2 (multiply with 2)
i.e. X : Y = 9 : 6 and
Y : Z = 6 : 4
∴ X : Y : Z = 9 : 6 : 4

Total Run scored by A, B and C = 342
Run Scored by A = $$\frac{9}{19} \times 342 = 162$$
Run Scored by B = $$\frac{6}{19} \times 342 = 108$$
Run Scored by C = $$\frac{4}{19} \times 342 = 72$$

82

Find the fraction which will bear the same ratio to $$\frac{1}{27}$$ that $$\frac{3}{11}$$ does to $$\frac{5}{9}$$

A) $$\frac{1}{{55}}$$ B) $$\frac{{15}}{{99}}$$ C) $$\frac{{40}}{{33}}$$ D) 55

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & = x:\frac{1}{{27}}::\frac{3}{{11}}:\frac{5}{9} \cr & \Rightarrow \frac{5}{9}x = \frac{1}{{27}} \times \frac{3}{{11}} = \frac{1}{{99}} \cr & \Rightarrow x = \frac{1}{{99}} \times \frac{9}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{{55}} \cr} $$

83

A, B, C and D have Rs. 40, Rs. 50, Rs. 60 and Rs. 70 respectively when they go to visit a fair. A spends Rs. 18, B spends Rs. 21, C spends Rs. 24 and D spends Rs. 27. Who has done the highest expenditure proportionate to his resources ?

A) A B) B C) C D) D

Discuss

Answer & Solution

Answer: Option A

Solution:

Ratio of the expenditures of A, B, C, D are as under:
$$\eqalign{ & {\text{A}} \to \frac{{18}}{{40}} = \frac{9}{{20}} = 0.45 \cr & {\text{B}} \to \frac{{21}}{{50}} = 0.42 \cr & {\text{C}} \to \frac{{24}}{{60}} = 0.4 \cr & {\text{D}} \to \frac{{27}}{7} = 0.385 \cr} $$
Clearly, A has done the highest expenditure proportionate to his resources.

84

Seema and Meena divide a sum of Rs. 25000 in the ratio of 3 : 2 respectively. If Rs. 5000 is added to each of their shares, what would be in the new ratio formed ?

A) 2 : 3 B) 3 : 4 C) 5 : 4 D) 4 : 3

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & {\text{Seema's share}} \cr & = {\text{Rs}}{\text{.}}\left( {25000 \times \frac{3}{5}} \right) \cr & = {\text{Rs}}.15000. \cr & {\text{Meena's share}} \cr & = {\text{Rs}}{\text{.}}\left( {25000 \times \frac{2}{5}} \right) \cr & = {\text{Rs}}.10000. \cr} $$
∴ Required ration
= (15000 + 5000) : (10000 + 5000)
= 4 : 3

85

A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a pair of black socks is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50% . The ratio of the number of black and brown pairs of socks in the original order was = ?

A) 2 : 1 B) 1 : 4 C) 1 : 2 D) 4 : 1

Discuss

Answer & Solution

Answer: Option B

Solution:

	Black	:	Brown
Pairs	4	:	x
Price	2	:	1
	8	:	x

Original bill = 8 + x

	Black	:	Brown
Pairs	x	:	4
Price	2	:	1
	2x	:	4

New bill = 2x + 4
According to the question,
$$\eqalign{ & \therefore {\text{3}}\left( {8 + x} \right) = 2\left( {2x + 4} \right) \cr & \Rightarrow 24 + 3x = 4x + 8 \cr & \Rightarrow x = 16 \cr & \therefore {\text{ Brown pairs}} = 16 \cr & \therefore {\text{Black pairs}} = 4 \cr & \therefore {\text{Ratio}} \Rightarrow 1:4 \cr} $$

86

The ratio of age of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be = ?

A) $$\frac{{22}}{{24}}$$ B) $$\frac{{15}}{{16}}$$ C) $$\frac{{17}}{{18}}$$ D) $$\frac{{11}}{{12}}$$

Discuss

Answer & Solution

Answer: Option C

Solution:

Ratio of ages of Boys A and B
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{A}}\,\,\,:\,\,\,{\text{B}} \cr & {\text{Present age }}5x\,\,\,:\,\,\,6x \cr & \therefore {\text{After two years }} \cr & \therefore \frac{{5x + 2}}{{6x + 2}} = \frac{7}{8} \cr & \Rightarrow 40x + 16 = 42x + 14 \cr & \Rightarrow 2x = 2 \cr & \Rightarrow x = 1 \cr & \therefore {\text{Present age }} \cr & {\text{A}} = 5 \times 1 = 5 \cr & {\text{B}} = 6 \times 1 = 6 \cr & {\text{After 12 years}} \cr & {\text{A}} = 5 + 12 = 17 \cr & {\text{B}} = 6 + 12 = 18 \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{{17}}{{18}} \cr} $$

87

A person divided Rs. 10800 among his three sons in the ratio 3 : 4 : 5. Second son kept Rs. 1000 for himself, gave Rs. 600 to his wife and divided the remaining money among his two daughters in the ratio 11 : 9. Then one of his daughters received.

A) Rs. 1000 B) Rs. 1050 C) Rs. 1100 D) Rs. 1150

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & {\text{Second son's share}} \cr & = {\text{Rs}}{\text{.}}\left( {10800 \times \frac{4}{{12}}} \right) \cr & = {\text{Rs}}{\text{. }}3600 \cr} $$
Money distributed between the two daughters
= Rs. [3600 - (1000 + 600)]
= Rs. 2000
$$\eqalign{ & {\text{First daughter's share}} \cr & = {\text{Rs}}{\text{.}}\left( {2000 \times \frac{{11}}{{20}}} \right) \cr & = {\text{Rs}}.1100. \cr & {\text{Second daughter's share}} \cr & = {\text{Rs}}{\text{.}}\left( {2000 \times \frac{9}{{20}}} \right) \cr & = {\text{Rs}}{\text{. 9}}00 \cr} $$

88

The numbers x, y, z are proportional to 2, 3, 5. The sum of x, y, z is 100. If y = px - 10, then p is equal to.

A) $$\frac{3}{2}$$ B) 2 C) $$\frac{5}{2}$$ D) 3

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & \to x:y:z = 2:3:5 \cr & \therefore x = \left( {100 \times \frac{2}{{10}}} \right) = 20 \cr & y = \left( {100 \times \frac{3}{{10}}} \right) = 30 \cr & y = px - 10 \cr & \Rightarrow 30 = 20p - 10 \cr & \Rightarrow 20p = 40 \cr & \Rightarrow p = 2 \cr} $$

89

Of three positive numbers, the ratio of first and second is 8 : 9, that of second and third is 3 : 4. The product of first and third is 2400. The sum of the three number is = ?

A) 145 B) 185 C) 295 D) 155

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{First}}:{\text{Second}}:{\text{Third}} \cr & \,\,\,\,8\,\,\,\,\,\,:\,\,\,\,\,\,9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3\,\,\,\,\,\,\,\,\,\,\,:\,\,\,\,\,4 \cr & \frac{{\overline {\,\,24\,\,\,:\,\,\,\,\,27\,\,\,\,\,\,\,\,:\,\,\,\,36} }}{{\underline {\,8\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,\,9\,\,\,\,\,\,\,\,:\,\,\,\,12} }} \cr & {\text{Let 8x}}:{\text{9x}}:{\text{12x}} \cr & \therefore {\text{First}} \times {\text{Third}} \cr & 8x \times 12x = 2400 \cr & \Rightarrow 96{x^2} = 2400 \cr & \Rightarrow {x^2} = \frac{{2400}}{{96}} = 25 \cr & \Rightarrow x = 5 \cr & \therefore {\text{Sum of three numbers }} \cr & {\text{First}} + {\text{Second}} + {\text{Third}} \cr & 8x + 9x + 12x = 29x \cr & \therefore 29 \times 5 = 145 \cr} $$

90

Three numbers are in the ratio 1 : 2 : 3. By adding 5 to each of them, the new numbers are in the ratio 2 : 3 : 4. The numbers are = ?

A) 10, 20, 30 B) 15, 30, 45 C) 1, 2, 3 D) 5, 10, 15

Discuss

Answer & Solution

Answer: Option D

Solution:

Let A, B and C is the number
∴ A : B : C = 1 : 2 : 3 = 1x : 2x : 3x
After adding 5 in each number new ratio of
A : B : C = 2 : 3 : 4 = 2x : 3x : 4x
∴ for A → 2x - 1x = 5
i.e x = 5
∴ A = 1 × 5 = 5,
B = 2 × 5 = 10 and
C = 3 × 5 = 15