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There are two numbers and their ratio is 3 : 9. If we substract 9 from both numbers then their ratio becomes 12 : 13, what is value is smaller number ?

  • 23
  • 27
  • 31
  • 33

Answer: Option D

Explanation:

From question, lets assume that two numbers are 3x and 5x.

\begin{aligned}
\text{then, }\frac{3x - 9}{ 5x - 9} = \frac{12}{23}\\
=> \text{23(3x - 9) = 12(5x - 9)}\\
=> 9x = 99 \\
=> x = 11
\end{aligned}
So numbers are 3(11) = 33, 5(11) = 55.
Smaller number is 33.

Similar Questions :

1. Find the fourth proportion to 2,3,6

  • 18
  • 12
  • 9
  • 4

Answer: Option C

Explanation:

2:3 :: 6:x

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

2. 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

  • 10
  • 17
  • 25
  • 30

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}

3. 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

  • 4:5
  • 9:5
  • 8:5
  • 9:2

Answer: Option B

Explanation:

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

4. If Rs. 782 is divided into three parts, proportional to
\begin{aligned}
\frac{1}{2}:\frac{2}{3}:\frac{3}{4}
\end{aligned}

find the first part.

  • 190
  • 204
  • 220
  • 230

Answer: Option B

Explanation:

\begin{aligned}
\frac{1}{2}:\frac{2}{3}:\frac{3}{4} \\
= 6:8:9\\
\text{First part =} 782 * \frac{6}{23} \\
= 204
\end{aligned}

5. 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}

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