Ratio - Aptitude MCQ Questions and Solutions with Explanations

Given, A : B = 6 : 5
B : C = 10 : 9
A : B = 6 : 5 (multiply with 2)
i.e. A : B = 12 : 10
∴ A : B : C = 12 : 10 : 9
⇒ 12x + 10x + 9x = 1280
⇒ x = 40
∴ Share of C = 9 × 40 = 360

$$\eqalign{ & = x:7.5 = 7:17.5 \cr & \Rightarrow 17.5x = 7.5 \times 7 \cr & \Rightarrow x = \frac{{7.5 \times 7}}{{17.5}} \cr & = 3 \cr} $$

$$\eqalign{ & = x:2\frac{1}{3}::21:50 \cr & \Rightarrow 50x = \frac{7}{3} \times 21 \cr & \Rightarrow 50x = 49 \cr & \Rightarrow x = \frac{{49}}{{50}} \cr} $$

$$\eqalign{ & = \sqrt 2 :\left( {1 + \sqrt 3 } \right)::\sqrt 6 :x \cr & \Rightarrow \sqrt {2}x = \sqrt 6 \left( {1 + \sqrt 3 } \right) \cr & \Rightarrow x = \frac{{\sqrt 6 \left( {1 + \sqrt 3 } \right)}}{{\sqrt 2 }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt 3 \left( {1 + \sqrt 3 } \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt 3 + 3 \cr} $$

The ratio of copper and zinc is 5 : 2
i.e 5x : 2x
Quantity of initial mixture = 17.5 kg
∴ 5x + 2x = $$\frac{35}{2}$$
⇒ x = $$\frac{5}{2}$$
Quantity of Copper in initial mixture
$$\eqalign{ & = \frac{5}{2} \times 5 \cr & = \frac{{25}}{2}kg \cr} $$
Quantity of Zinc in initial mixture
$$\eqalign{ & = \frac{5}{2} \times 2 \cr & = 5\,kg \cr} $$
Now after adding 1.250 kg of zinc
= 5 + 1.250
= 6.250 kg
= $$\frac{{25}}{4}kg$$
∴ New Ratio of copper : zinc
$$\eqalign{ & = \frac{{25}}{2}:\frac{{25}}{4} \cr & = 2:1 \cr} $$

Let income of A, B and C are 7x, 9x and 12x respectively
and expenditure of A, B and C are 8y, 9y and 15y respectively
$$\eqalign{ & \Rightarrow {\text{Income}}\,{\text{of,}} \cr & A \times \frac{1}{4} = {\text{Saving}}\,{\text{of}}\,{\text{A}}\,\left( {{\text{given}}} \right) \cr & \Rightarrow 7x - 8y = 7x \times \frac{1}{4} \cr & \Rightarrow 28x - 32y = 7x \cr & \Rightarrow 21x = 32y \cr & \Rightarrow x:y = 32:21 \cr} $$
∴ The ratio of savings of A, B and C
⇒ (7x - 8y) : (9x - 9y) : (12x - 15y)
⇒ (7 × 32 - 8 × 21) : (9 × 32 - 9 × 21) : (12 × 32 - 15 × 21)
⇒ (224 - 168) : (288 - 189) : (384 - 315)
⇒ 56 : 99 : 69

1 day = 24 hours.
∴ Given ration = 3 : 24
= 1 : 8

Product of 1^st and 4^th terms (extremes) = product of 2^nd and 3^rd terms (means)
$$\eqalign{ & \Rightarrow {\text{2}}{\text{.5}}x = {\text{40}} \cr & \Rightarrow x = \frac{{40}}{{2.5}} = 16 \cr} $$

$$\eqalign{ & 20\% \,{\text{of A}} = 30\% \,{\text{of B}} = \frac{1}{6}{\text{of C}} \cr & \Rightarrow \frac{{20{\text{A}}}}{{100}} = \frac{{30{\text{B}}}}{{100}} = \frac{{\text{C}}}{{\text{6}}} \cr & \Rightarrow \frac{{\text{A}}}{5} = \frac{{3{\text{B}}}}{{10}} = \frac{C}{6} = k(say) \cr & \Rightarrow A = 5K,\,B = \frac{{10k}}{3},\,C = 6k \cr & \therefore {\text{A}}:{\text{B}}:{\text{C}} = 5k:\frac{{10k}}{3}:6k \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5:\frac{{10}}{3}:6 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15:10:18 \cr} $$

$$\eqalign{ & {\text{A}}:{\text{B}} \cr & 17:45 \cr & 17x:45x \cr & {\text{Given}} \cr & \Rightarrow 17x \times \frac{1}{3} + 15 = 45x \times \frac{1}{5} \cr & \Rightarrow \frac{{17x + 45}}{3} = 9x \cr & \Rightarrow 17x + 45 = 27x \cr & \Rightarrow 10x = 45 \cr & \Rightarrow x = \frac{{45}}{{10}} \cr & \therefore {\text{Smaller number is }} \cr & = \frac{{45}}{{10}} \times 17 \cr & = \frac{{765}}{{10}} \cr & = 76\frac{1}{2} \cr} $$