Ratio - Aptitude MCQ Questions and Solutions with Explanations

Let the first number be x and second number be y
According to the question,
$$\eqalign{ & 80\% {\text{ of }}x = \frac{4}{5}\,{\text{of }}y \cr & \Rightarrow \frac{{80 \times x}}{{100}} = \frac{{4 \times y}}{5} \cr & \Rightarrow \frac{{4x}}{5} = \frac{{4y}}{5} \cr & \Rightarrow x:y = 1:1 \cr} $$

Let the monthly salary of Pia and Som be 5a and 4a respectively.
Then,
Money given by Pia to her mother
$$\eqalign{ & = 5a \times \frac{3}{5} = 3a \cr } $$
Money given by Pia as sister's tuition fees
$$\eqalign{ & = 15\% {\text{ of }}5a \cr & = \frac{{15 \times 5a}}{{100}} \cr & = \frac{{75a}}{{100}} = 0.75a \cr} $$
Money given by Pia towards loan
$$\eqalign{ & = 18\% {\text{ of }}5a \cr & = \frac{{18 \times 5a}}{{100}} \cr & = \frac{{90a}}{{100}} = 0.9a \cr & \therefore {\text{Total money given}} \cr & = 3a + 0.75a + 0.90a \cr & = 4.65a \cr & \therefore {\text{Remaining amount}} \cr & = 5a - 4.65 \cr & = 0.35a \cr & {\text{Pia have remaining amount}} \cr & = {\text{Rs}}{\text{. }}2100 \cr & 0.35a = 2100 \cr & \therefore \frac{{35a}}{{100}} = 2100 \cr & \Rightarrow a = \frac{{2100 \times 100}}{{35}} \cr & a = {\text{Rs}}{\text{. }}6000 \cr & \therefore {\text{Monthly salary of Som}} \cr & = 4a = 4 \times 6000 \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}24000 \cr} $$

Let 1 bottle of acid is 30litre and consider the first bottle as A and second bottle as B.
Ratio of Acid and water in bottle A = 2 : 3
Volume of Acid in bottle A = $$\frac{2}{5} \times 30 = 12$$
Volume of Water in bottle A = $$\frac{3}{5} \times 30 = 18$$

Ratio of Acid and water in bottle A = 1 : 2
Volume of Acid in bottle A = $$\frac{1}{3} \times 30 = 10$$
Volume of Water in bottle A = $$\frac{2}{3} \times 30 = 20$$

Now 1 bottle of A and 3 bottles of B mixed together

Volume of Acid in new mixture = 12 + 3 × 10 = 42
Volume of water in new mixture = 18 + 3 × 20 = 78
Ratio of Acid and water in new mixture = 42 : 78 = 7 : 13

Given, blue and yellow color ratio = 4 : 3 and half part blue and yello ratio = 2 : 3

Let 700 be the painting part in total
∴ Blue part will be: $$\frac{{\text{4}}}{7} \times 700$$   = 400
And yellow will be: $$\frac{{\text{3}}}{7} \times 700$$   = 300
Now, upper half part i.e $$\frac{{700}}{2}$$ = 350
Blue in upper half part → $$\frac{{\text{2}}}{5} \times 350$$   = 140
And, Yellow in upper half part → $$\frac{{\text{3}}}{5} \times 350$$   = 210
Remaining half Blue in lower part → 400 - 140 = 260
Remaining half yellow in lower part → 300 - 90 = 210
Ratio of blue and yellow → 260 : 90
⇒ 26 : 9

Ratio of the number of 50 paisa, 25 paisa and 10 paisa coins = 5 : 8 : 3
Ratio of their values
$$\eqalign{ & = \frac{5}{8}:\frac{8}{4}:\frac{3}{{10}} \cr & {\text{LCM of 2, 4 and 10}} = 20 \cr & = \left( {\frac{5}{2} \times 20} \right):\left( {\frac{8}{4} \times 20} \right):\left( {\frac{3}{{10}} \times 20} \right) \cr & = 50:40:6 \cr & {\text{Sum of the terms of ratio}} \cr & = 50 + 40 + 6 = 96 \cr & \therefore {\text{Value of 50 paisa coins}} \cr & = \frac{{50}}{{96}} \times 144 = 75 \cr & \therefore {\text{Number of 50 paisa coins}} \cr & = 75 \times 2 = 150 \cr} $$

$$\eqalign{ & {\text{Given}} \cr & \frac{7}{5}{\text{of }}58 + \frac{3}{8}{\text{of }}139.2 = ? \cr & = \frac{7}{5} \times 58 + \frac{3}{8} \times 139.2 \cr & = 81.2 + 52.2 \cr & = 133.4 \cr} $$

Let the number of spectators on Monday, Tuesday and Wednesday be 2p, 3p and 5p respectively.
Let the price charged on Monday, Tuesday and Wednesday be 2q, 3q and 4q respectively.
According to the question,
4q × 5p × 3p = 8800
⇒ 20pq - 9pq = 8800
⇒ 11pq = 8800
⇒ pq = 800
Now, total amount earned on all three days
= 4pq + 9pq + 20pq
= 4 × 800 + 9 × 800 + 20 × 800
= Rs. (3200 + 7200 + 16000)
= Rs. 26400

$$\eqalign{ & {\text{Let denominator}} = x \cr & {\text{Numerator}} = x + 3 \cr & {\text{Fraction become}} = \frac{{x + 3}}{x} \cr & {\text{According to the question,}} \cr & \frac{{x + 3 + 5}}{{x - 2}} = \frac{8}{3} \cr & 3x + 24 = 8x - 16 \cr & 5x = 40 \cr & x = 8 \cr & \therefore {\text{Denominator}} = 8 \cr & {\text{Numerator}} = 8 + 3 = 11 \cr & {\text{Fraction}} = \frac{{11}}{8} \cr & {\text{Then, }}\frac{{11}}{8} \div \frac{{11}}{2} = \frac{{11}}{8} \times \frac{2}{{11}} = \frac{1}{4} \cr} $$

\[\begin{array}{*{20}{c}} {}&{{\text{Last year}}}&{{\text{Current year}}} \\ {{\text{A}} \to }&{{4_{ \times 1 \times 5}} = 20}&{{5_{ \times 1 \times 5}} = 25} \\ {{\text{B}} \to }&{{2_{ \times 2 \times 4}} = 16}&{{3_{ \times 2 \times 4}} = 24} \end{array}\]
Ratio of final year income of A and B. So because we taken income 20, 16
Ratio of present age of both = 25 : 24
Sum of present age of both = 25 + 24 = 49 units
49 units → 705600
1 unit → 14400
24 units → 14400 × 24 = 345600
B's income is 2021 = 345600

Alternate solution
\[\begin{array}{*{20}{c}} {}&{\text{A}}&:&{\text{B}} \\ {{\text{Previous year}} \to }&{5x}&:&{4x} \end{array}\]
A's present income : final year and present year = 4 : 5
4 units = 5x
5 units = 5x × $$\frac{5}{4}$$ = $$\frac{{25}}{4}$$x
B's present income : final year and present year = 2 : 3
2 units = 4x
3 units = 3x × $$\frac{4}{2}$$ = 6x
\[\begin{array}{*{20}{c}} {}&{\text{A}}&:&{\text{B}} \\ {{\text{Present year}} \to }&{\frac{{25}}{4}x}&:&{6x} \end{array}\]
$$\frac{{25}}{4}$$x + 6x = $$\frac{{49}}{4}$$x → 705600
x = 14400 × 4 = 57600
B's income = 6x = 6 × 57600 = 345600
B's income in 2021 = 345600

$$\eqalign{ & A \to 3:4 = {7_{ \times 2 \times 2}} \cr & B \to 5:9 = {14_{ \times 3}} \cr & {\text{Copper}}:{\text{Zinc}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,{\text{12}}\,\,\,{\text{:}}\,\,\,{\text{16}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,{\text{15}}\,\,\,{\text{:}}\,\,\,{\text{27}} \cr & \,\,\,\,\,\,\,\,\,\,\overline {\,\,27\,:\,43\,\,} \cr} $$