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Question Detail
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.
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
- 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}
2. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number.
- 2:5
- 2:7
- 5:7
- 5:3
Answer: Option D
Explanation:
Let the first number is A and second number is B.
As per question
\begin{aligned}
\frac{40}{100}A = \frac{2}{3}B \\
\frac{A}{B} = \frac{2}{3}*\frac{100}{40} \\
\frac{A}{B} = \frac{5}{3} \\
=> A:B = 5:3
\end{aligned}
3. In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is
- 20 liters
- 30 liters
- 50 liters
- 60 liters
Answer: Option D
Explanation:
Quantity of Milk = 60*(2/3) = 40 liters
Quantity of water = 60-40 = 20 liters
As per question we need to add water to get quantity 2:1
=> 40/(20+x) = 1/2
=> 20 + x = 80
=> x = 60 liters
4. If A:B:C = 2:3:4, then find
\begin{aligned}
\frac{A}{B}:\frac{B}{C}:\frac{C}{A}
\end{aligned}
- 5:9:24
- 6:9:24
- 7:9:24
- 8:9:24
Answer: Option D
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}
5. Rs. 120 are divided among A, B, C such that A's share is Rs. 20 more than B's and Rs. 20 less than C's. What is B's share
- Rs 10
- Rs 20
- Rs 24
- Rs 28
Answer: Option B
Explanation:
Let C = x. Then A = (x—20) and B = (x—40).
x + x - 20 + x - 40 = 120 Or x=60.
A:B:C = 40:20:60 = 2:1 :3.
B's share = Rs. 120*(1/6) = Rs. 20
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