Ratio - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Let C gets }}x{\text{ rupees}} \cr & \therefore {\text{B gets }}x + 8{\text{ rupees}} \cr & \therefore {\text{A gets }}x + 8 + 7{\text{ rupees}} \cr & {\text{Total A}} + {\text{B}} + {\text{C}} \cr & \Rightarrow x + 15 + x + 8 + x = 3x + 23 \cr & \Rightarrow 3x + 23 = {\text{Rs}}{\text{. }}53({\text{given)}} \cr & \Rightarrow 3x = 30 \cr & \Rightarrow x = 10 \cr & \Rightarrow x = {\text{Rs}}{\text{.10}} \cr & \therefore {\text{Ratio of their shares is }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{A}}\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,{\text{B}}\,\,\,\,\,\,\,\,:\,\,\,{\text{C}} \cr & {\text{ = }}\left( {x + 15} \right):\left( {x + 8} \right):\left( x \right) \cr & = \,\,\,\,\,\,\,\,\,25\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,18\,\,\,\,\,:\,\,10 \cr} $$

$$\eqalign{ & {\text{Remainder}} \cr & = {\text{Rs}}{\text{.}}\left[ {{\text{1087}} - \left( {10 + 12 + 15} \right)} \right] \cr & = {\text{Rs}}{\text{. }}1050. \cr & \therefore {\text{B's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {1050 \times \frac{7}{{21}}} \right) + 12} \right] \cr & = {\text{Rs}}{\text{. }}362 \cr} $$

Let x = 5k and y = 7k
Then,
= x + y = 36 ⇒ 5k + 7k = 36
⇒ 12k = 36
⇒ k = 3
∴ x = 5k = 5 × 3 = 15

Let the numbers be 3x and 5x
Then,
= 3x × 5x = 2160
⇒ 15x² = 2160
⇒ x² = 144
⇒ x = 12
∴ Smaller number = 3x = 3 × 12 = 36

$$\eqalign{ & \Rightarrow \frac{1}{2}{\text{A}} = \frac{1}{3}{\text{B}} = \frac{1}{4}{\text{C}} \cr & \Rightarrow {\text{A}}:{\text{B}}:{\text{C}} \cr & \,\,\,\,\,\,\,\,2\,\,:3:4{\text{ }} \cr & 2x + 3x + 4x = 900 \cr & \Rightarrow 9x = 900 \cr & \Rightarrow x = 100 \cr & {\text{A}} = 200 \cr & {\text{B}} = 300 \cr & {\text{C}} = 400 \cr} $$

$$\eqalign{ & \Rightarrow {\text{A}}:{\text{B}}:{\text{C}} \cr & \,\,\,\,\,\,\,\,\,2:5:4{\text{ }} \cr & 2x + 5x + 4x = 11x \cr & \Rightarrow 11x = {\text{Rs}}.126.50 \cr & \Rightarrow x = {\text{Rs}}{\text{.11}}{\text{.50}} \cr & \Rightarrow {\text{Share of B}} = 5x \cr & \Rightarrow {\text{Share of A}} = 2x \cr & \therefore {\text{Share of (B}} - {\text{A)}} = 3x \cr & \Rightarrow 3 \times 11.50 = {\text{Rs}}. 34.50 \cr} $$

Let C gets x rupees
∴ B gets x + 6 rupees
∴ A gets x + 6 + 7 rupees
Total A + B + C ⇒ (3x + 19)
⇒ 3x + 19 = Rs. 76
⇒ 3x = 76 - 19
⇒ 3x = 57
⇒ x = 19
A gets = 19 + 13 = Rs. 32
B gets = 19 + 6 = Rs. 25
C gets = Rs. 19
∴ A : B : C
= 32 : 25 : 19

Let the shares of A, B, C and D be Rs. 3x, 4x, 9x and 10x respectively.
= 9x - 4x =2580
⇒ 5x = 2580
⇒ x = 516
∴ Required Amount = 3x + 10x = 13x
= Rs. (13 × 516)
= Rs. 6708

$$\eqalign{ & {\text{Ram}}:{\text{Shyam}} = 7:17 \cr & {\text{Shyam}}:{\text{Sohan}} = 7:17 \cr & = \left( {7 \times \frac{{17}}{7}} \right):\left( {17 \times \frac{{17}}{7}} \right) \cr & = 17:\frac{{289}}{7} \cr & {\text{Ram}}:{\text{Shyam}}:{\text{Sohan}} \cr & = 7:17:\frac{{289}}{7} \cr & = 49:119:289 \cr} $$
Let Sohan's income be Rs. x
Then,
= 49 : 289 :: 490 : x or x = 2890

$$\eqalign{ & {\text{Ratio of sides}} \cr & = \frac{{\text{1}}}{{\text{2}}}:\frac{{\text{1}}}{{\text{3}}}:\frac{{\text{1}}}{{\text{4}}} \cr & = 6:4:3 \cr} $$
Let the sides be 6x, 4x and 3x
Then,
⇒ 6x + 4x + 3x = 104
or 13x = 104
or x = 8
∴ Longest side = 6x = (6 × 8)m = 48m