Ratio - Aptitude MCQ Questions and Solutions with Explanations

Let total student = 12 unit
B : G
7 : 5
B → $$\frac{4}{7}$$   (14 year less)
B = 4   (14 year less)
G → $$\frac{2}{5}$$
G = 3   (14 year less)
Total student less than 14 year = 4 + 3 = 7
7 → 1120
1 → 160
12 → 1920 total student

Let, each term be 16a and 19a, and the number subtracted from it is x.
$$\frac{{16a - x}}{{19a - x}} = \frac{7}{6}$$
⇒ 96a - 6x = 133a - 7x
⇒ x = 133a - 96a
⇒ x = 37a
Hence, the number will be the multiple of 37.
So, from option A is a right answer.

Third proportional of 16 and 24 $$ = \frac{{{b^2}}}{a} = \frac{{24 \times 24}}{{16}} = 36$$

Let the salary of Vipin and Dinesh be 5$$x$$ and 8$$x$$
$$\eqalign{ & \frac{{5x + 4800}}{{8x + 4800}} = \frac{7}{{10}} \cr & \Rightarrow 50x + 48000 = 56x + 33600 \cr & \Rightarrow x = \frac{{14400}}{6} \cr & \Rightarrow x = 2400 \cr} $$
∴ Vipin's salary is Rs. 12000

$$\eqalign{ & \frac{l}{{2\left( {l + b} \right)}} = \frac{2}{7} \cr & \Rightarrow 7l = 4l + 4b \cr & \Rightarrow 3l = 4b \cr & \Rightarrow \frac{l}{b} = \frac{4}{3} = 4:3 \cr} $$

\[\begin{array}{*{20}{c}} {}&{{\text{Last year}}}&{{\text{Current year}}} \\ {{\text{A}} \to }&{{3_{ \times 5 \times 4}} = 60}&{{4_{ \times 5 \times 4}} = 80} \\ {{\text{B}} \to }&{{5_{ \times 3 \times 3}} = 45}&{{6_{ \times 3 \times 3}} = 54} \end{array}\]
The ratio of income of A and B in the last year is 4 : 3. So we're making last year's income 60, 45.
Present age ratio of both = 80 : 54
Sum of present age of both = 80 + 54 = 134 units
134 units → 24.12 lakh
1 unit → $$\frac{{24.12}}{{134}}$$
Sum of income of A in final year and income of B in present year = 60 + 54 = 114
114 units → $$\frac{{24.12}}{{134}}$$ × 114 = 20.52
Sum of income of A in final year and income of B in present year = 20.52 lakh

Alternate solution
\[\begin{array}{*{20}{c}} {}&{\text{A}}&{\text{B}} \\ {{\text{Previous year }} \to }&{4x}&{3x} \end{array}\]
A's present salary : Ratio of final year to present year = 3 : 4
3 units = 4x
4 units $$ = 4x \times \frac{4}{3} = \frac{{16}}{3}x$$
B's present salary : Final year and present year = 5 : 6
5 units = 3x
6 units $$ = 3x \times \frac{6}{5} = \frac{{18}}{5}x$$
\[\begin{array}{*{20}{c}} {}&{{\text{A}}\,\,\,}&{{\text{B}}\,\,\,} \\ {{\text{Present year }} \to }&{\frac{{16}}{3}x}&{\frac{{18}}{5}x} \end{array}\]
$$\eqalign{ & \frac{{16}}{3}x + \frac{{18}}{5}x = \frac{{134}}{{15}}x \to 24.12{\text{ lakh}} \cr & x = \frac{{24.12 \times 15}}{{134}} \cr} $$
Final year income of A and Present year income of B.
$$\eqalign{ & = 4x + \frac{{18}}{5}x = \frac{{38}}{5}x \cr & \frac{{38}}{5}x \to \frac{{24.12 \times 15}}{{134}} \times \frac{{38}}{5} = 20.52 \cr} $$
Final year income of A and Present year income of B = 20.52 lakh

\[\begin{array}{*{20}{c}} {}&{{\text{Rs}}{\text{. 1}}}&:&{{\text{Rs}}{\text{. 5}}}&:&{{\text{Rs}}{\text{. 10}}}&{} \\ {{\text{Number of notes}}}&1&:&1&:&1&{} \\ {}&x&:&x&:&x&{ = \boxed{3x}{\text{ number of notes}}} \\ {{\text{So, Value}}}&x&:&{5x}&:&{10x}&{ = \boxed{16x}{\text{ value of notes}}} \end{array}\]
$$\eqalign{ & x + 5x + 10x = 640 \cr & 16x = 640 \cr & \boxed{x = 40} \cr & \therefore {\text{Number of notes }}40 \times 3 = 120 \cr} $$

Ratio of shares of Seema and Komal = 1.5x : 2x
Ratio of shares of Komal and Rita = 2x : 2.5x
Ratio of shares of Seema, Komal and Rita = 1.5x : 2x : 2.5x
According to the question
1.5x + 2x + 2.5x = 3600
⇒ 6x = 3600
⇒ x = $$\frac{{3600}}{6}$$
⇒ x = 600
∴ Share of Rita = 2.5 × 600 = Rs. 1,500

\[\begin{array}{*{20}{c}} {{\text{Male}}}&{}&{{\text{Female}}}&{}&{} \\ \begin{gathered} 5 \hfill \\ \,\,\,\,\,\,\,{ \downarrow ^{ \times 50}} \hfill \\ 250 \hfill \\ \end{gathered} &\begin{gathered} : \hfill \\ \hfill \\ \hfill \\ \end{gathered} &\begin{gathered} 3 \hfill \\ \,\,\,\,\,\,\,{ \downarrow ^{ \times 50}} \hfill \\ 150 \hfill \\ \end{gathered} &\begin{gathered} \to \hfill \\ \hfill \\ \hfill \\ \end{gathered} &\begin{gathered} 8 - 400 \hfill \\ 1 - 50 \hfill \\ \hfill \\ \end{gathered} \end{array}\]
Total regular employees = 400 × 87.5%
= 400 × $$\frac{{875}}{{100 \times 10}}$$  = 350
Regular male employees = 250 × 92%
= 250 × $$\frac{{92}}{{100}}$$ = 230
∴ Regular female employees = 350 - 230 = 120
∴ % of regular female employees = $$\frac{{120}}{{150}}$$ × 100% = 80%

\[\begin{array}{*{20}{c}} {}&{{\text{Rs}}{\text{. 2}}}&{}&{{\text{50 Paise }}}&{}&{{\text{25 Paise}}} \\ {{\text{Coins}}}&3&:&5&:&7 \end{array}\]
Amount = Number of coins × Face value
Amount = $$6:\frac{5}{2}:\frac{7}{4}$$
According to question,
$$\eqalign{ & \Rightarrow 6x + \frac{{5x}}{2} + \frac{{7x}}{4} = 51.25 \cr & \Rightarrow 24x + 10x + 7x = 51.25 \times 4 \cr & \Rightarrow 41x = 205 \cr & \Rightarrow x = \frac{{205}}{{41}} \cr & \boxed{x = 5} \cr} $$
∴ Total number of 50 paise coins = 5 × 5 = 25