Question Detail

If a:b = 2:3 and b:c = 4:3, then find a:b:c

8:12:9
2:3:8
2:3:9
2:3:12

Answer: Option A

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. The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of the second to the third is 5:8, then the second number is

Answer: Option D

Explanation:

\begin{aligned}
a:b = 2:3 \\
b:c = 5:8 = (5*\frac{3}{5} : 8*\frac{3}{5}) \\
= 3:\frac{24}{5} \\
a:b:c = 2:3:\frac{24}{5} \\
= 10:15:24 \\
b = 98*\frac{15}{49} \\
= 30
\end{aligned}

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

Answer: Option C

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

3. If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

Answer: Option B

Explanation:

Let the numbers be 3x, 2x and 5x.
Then,
9x + 4x + 25x =1862
⇒ 38x = 1862
⇒ x = 49 ⇒ x = 7.
middle number = 2x = 14

4. A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is

Answer: Option B

Explanation:

Dog : Hare = (3*3) leaps of hare : 5 leaps of hare
= 9 : 5

5. 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.

20:33:60
21:33:60
22:33:60
23:33:60

Answer: Option D

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}