# Ratio and Proportion Questions Answers

• #### 1. If a:b = 2:3 and b:c = 4:3, then find a:b:c

1. 8:12:9
2. 2:3:8
3. 2:3:9
4. 2:3:12

Explanation:

\begin{aligned}
a:b = 2:3 \\
b:c = 4:3 = (4*\frac{3}{4} : 3*\frac{3}{4}) \\
= 3:\frac{9}{4} \\
a:b:c = 2:3:\frac{9}{4} \\
= 8:12:9
\end{aligned}

1. 18
2. 12
3. 9
4. 4

Explanation:

2:3 :: 6:x

=> 2/3 = 6/x
=> x = 18/2
=> x = 9

• #### 3. If A:B:C = 2:3:4, then find \begin{aligned} \frac{A}{B}:\frac{B}{C}:\frac{C}{A} \end{aligned}

1. 5:9:24
2. 6:9:24
3. 7:9:24
4. 8:9:24

Explanation:

Let A = 2x, B = 3x, C = 4x, then,
\begin{aligned}
\frac{A}{B} = \frac{2x}{3x} = \frac{2}{3} \\
\frac{B}{C} = \frac{3x}{4x} = \frac{3}{4} \\
\frac{C}{A} = \frac{4x}{2x} = \frac{2}{1} \\

=> \frac{A}{B}:\frac{B}{C}:\frac{C}{A} \\
= \frac{2}{3}:\frac{3}{4}:\frac{2}{1} \\
= 8:9:24

\end{aligned}

• #### 4. If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then find the value of A:B:C:D

1. 15:24:30:35
2. 16:24:30:35
3. 17:24:30:35
4. 18:24:30:35

Explanation:

\begin{aligned}
A:B = 2:3 \\
B:C = 4:5 = (4*\frac{3}{4} : 5*\frac{3}{4}) \\
= 3:\frac{15}{4} \\
C:D = 6:7 = (6*\frac{15}{24} : 7*\frac{15}{24}) \\
= \frac{15}{4}:\frac{35}{8} \\
A:B:C:D = 2:3:\frac{15}{4}:\frac{35}{8} \\
= 16:24:30:35
= 8:12:9
\end{aligned}

• #### 5. If 2 : 9 :: x : 18, then find the value of x

1. 2
2. 3
3. 4
4. 6

Explanation:

Treat 2:9 as 2/9 and x:18 as x/18, treat :: as =

So we get 2/9 = x/18
=> 9x = 36
=> x = 4

• #### 6. if x:y = 1:3, then find the value of (7x+3y):(2x+y)

1. 14:5
2. 15:5
3. 16:5
4. 17:5

Explanation:

let x = 1k and y = 3k, so
\begin{aligned}
= \frac{7(k)+3(3k)}{2(k)+1(3k)} \\
= \frac{16k}{5k} \\
= 16:5
\end{aligned}

• #### 7. The salaries of A, B and C are of ratio 2:3:5. If the increments of 15%, 10% and 20% are done to their respective salaries, then find the new ratio of their salaries.

1. 20:33:60
2. 21:33:60
3. 22:33:60
4. 23:33:60

Explanation:

Let A salary be 2k
B salary be 3k and C salary be 5k

\begin{aligned}
\text{A's new salary = }\frac{115}{100}*2k \\
= \frac{23}{10}k \\
\text{B's new salary = }\frac{110}{100}*3k \\
= \frac{33}{10}k \\
\text{C's new salary = }\frac{120}{100}*5k \\
= 6k \\

\text{New ratio = }\\
\frac{23k}{10}:\frac{33k}{10}:6k \\
= 23:33:60 \\
\end{aligned}