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Ratio - Aptitude MCQ Questions and Solutions with Explanations

Ratio MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Ratio with easy and logical explanations. Ratio MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-1 section-2

Each section contains 100 MCQs on Ratio .
1
If A : B = $$\frac{1}{2}$$ : $$\frac{3}{8},$$  B : C = $$\frac{1}{3}$$ : $$\frac{5}{9}$$ and C : D = $$\frac{5}{6}$$ : $$\frac{3}{4},$$  then the ratio A : B : C : D is
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{A}}:{\text{B}} = \frac{1}{2}:\frac{3}{8} = 4:3, \cr & {\text{B}}:{\text{C}} = \frac{1}{3}:\frac{5}{9} = 3:5, \cr & {\text{C}}:{\text{D}} = \frac{5}{6}:\frac{3}{4} = 10:9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5:\frac{9}{2}. \cr & \therefore {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & = 4:3:5:\frac{9}{2} \cr & = 8:6:10:9. \cr} $$
2
If p : q : r = 1 : 2 : 4, then $$\sqrt {5{p^2} + {q^2} + {r^2}} $$     is equal to =
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{p}}:{\text{q}}:{\text{r}} \cr & 1:2:4 \cr & x:2x:4x \cr & \therefore \sqrt {5{p^2} + {q^2} + {r^2}} \cr & = \sqrt {5{x^2} + 4{x^2} + 16{x^2}} \cr & = \sqrt {25{x^2}} \cr & = 5x \cr & = 5p \cr} $$
3
The mean proportion between $$\left( {3 + \sqrt 2 } \right)$$   and $$\left( {12 - \sqrt {32} } \right)$$   is = ?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & \left( {3 + \sqrt 2 } \right):x:\left( {12 - \sqrt {32} } \right) \cr & a:b:c \cr & {\text{mean proportion}} \cr & \Rightarrow {b^2} = a \times c \cr & \Rightarrow {x^2} = \left( {3 + \sqrt 2 } \right) \times \left( {12 - \sqrt {32} } \right) \cr & \Rightarrow {x^2} = \left( {3 + \sqrt 2 } \right) \times \left( {12 - 4\sqrt 2 } \right) \cr & \Rightarrow {x^2} = \left( {3 + \sqrt 2 } \right) \times 4\left( {3 - \sqrt 2 } \right) \cr & \Rightarrow {x^2} = 4 \times \left\{ {{{\left( 3 \right)}^2} - {{\left( {\sqrt 2 } \right)}^2}} \right\} \cr & \Rightarrow {x^2} = 28 \cr & \Rightarrow x = 2\sqrt 7 \cr} $$
4
a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is = ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & a:b:c \cr & 2:3:4 \cr & {\text{Let }}2x:3x:4x \cr & \Rightarrow 2a - 3b + 4c = 33 \cr & \Rightarrow 2 \times 2x - 3 \times 3x + 4 \times 4x = 33 \cr & \Rightarrow 4x - 9x + 16x = 33 \cr & \Rightarrow 11x = 33 \cr & \Rightarrow x = 3 \cr & \therefore {\text{c}} \Rightarrow 4 \times 3 = 12 \cr} $$
5
In a ratio which is equal to 7 : 8, if the antecedent is 35, what is the consequent?
Discuss
Answer & Solution
Answer: Option B
Solution:
Let the consequent be x
$$\eqalign{ & {\text{Then,}} \cr & \frac{7}{8} = \frac{{35}}{x} \Rightarrow 35 \times 8 \cr & \Rightarrow x = \frac{{35 \times 8}}{7} = 40 \cr} $$
6
If 8a = 9b then the ratio of $$\frac{{\text{a}}}{9}$$ to $$\frac{{\text{b}}}{8}$$ is
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & = {\text{8a}} = {\text{9b}} \Rightarrow a = \frac{9}{8}b \cr & \therefore \frac{{\text{a}}}{{\text{9}}}:\frac{{\text{b}}}{{\text{8}}} = \frac{{\left( {\frac{9}{8}b} \right)}}{9}:\frac{{\text{b}}}{{\text{8}}} \cr & = \frac{{\text{b}}}{{\text{8}}}:\frac{{\text{b}}}{{\text{8}}} = 1:1 \cr} $$
7
If x : y = 3 : 4, then (2x + 3y) : (3y - 2x) would be equal to.`
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & = \frac{x}{y} = \frac{3}{4} \cr & = \frac{{2x + 3y}}{{3y - 2x}} \cr & = \frac{{2\left( {\frac{x}{y}} \right) + 3}}{{3 - 2\left( {\frac{x}{y}} \right)}} \cr & = \frac{{2 \times \frac{3}{4} + 3}}{{3 - 2 \times \frac{3}{4}}} \cr & = \frac{9}{2} \times \frac{2}{3} = 3 \cr & = \left( {2x + 3y} \right):\left( {3y - 2x} \right) \cr & = 3:1 \cr} $$
8
Rs. 33630 are divided among A, B and C in such a manner that the ratio of the amount of A to that of B is 3 : 7 and the ratio of the amount of B to that of C is 6 : 5. The amount of money received by B is = ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Given, A : B = 3 : 7
B : C = 6 : 5
A : B = 3 : 7 (multiply with 6) and
B : C = 6 : 5 (multiply with 7)
i.e. A : B = 18 : 42 and
      B : C = 42 : 35
∴ A : B : C = 18 : 42 : 35
⇒18x + 42x + 35x = 33630
⇒ x = 354
∴ Money received by B = 42 × 354 = Rs. 14868
9
200 litres of a mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was =?
Discuss
Answer & Solution
Answer: Option B
Solution:
Milk : water = 17 : 3 = 17x : 3x
∴ 17x + 3x = 200
⇒ x =10 litre
Milk = 170 litre and water = 30 litre in initial mixture.
Let 'y' litre of milk added in mixture
i.e. 170 + y : 30 = 7 : 1
⇒ $$\frac{{170 + y}}{{30}} = \frac{7}{1}$$
∴ y = 210 - 170 = 40 litre
10
In an innings of a cricket match,three players A, B and C scored a total of 361 runs. If the ratio of the number of runs scored by A to that scored by B and also number of runs scored by B to that scored by C be 3 : 2, the number of runs scored by A was = ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Given total runs of A, B, C
(A + B + C = 361)
$$\eqalign{ & \Rightarrow {\text{A}}:{\text{B}}:{\text{C}} \cr & \,\,\,\,\,\,\,\,\,3:2 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3:2 \cr & \underline {\overline {\,\,\,\,\,\,\,\,\,\,9:6:4{\text{ }}} } \cr & \therefore 9x + 6x + 4x = 361 \cr & \Rightarrow 19x = 361 \cr & \Rightarrow x = 19 \cr & \therefore {\text{Runs scored by A }} \cr & = 9x \cr & = 9 \times 19 \cr & = 171 \cr} $$