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. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number.

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}

2. A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount. How much amount B have.

Rs 484
Rs. 480
Rs 478
Rs 470

Answer: Option A

Explanation:

In this type of question, we will first try to calculate the ratio of two persons. Once we get ratio then we can easily get our answer. So lets solve this.

\begin{aligned}
\frac{4}{15}A = \frac{2}{5}B \\
A = \left(\frac{2}{5}*\frac{14}{4}\right)B \\
A = \frac{3}{2}B \\
\frac{A}{B} = \frac{3}{2} \\
A:B = 3:2 \\
\text{B's Share = }\frac{2}{5}*1210 = 484
\end{aligned}

3. The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is

Answer: Option A

Explanation:

Let x is subtracted.
Then,
\begin{aligned}
\frac{(6-x)}{(7-x)}< \frac{16}{21} \\

21(6—x) < 16(7—x)\\
=> 5x > 14 = x > 2.8
\end{aligned}

Least such number is 3

4. 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 ?

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.

5. Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs 4000, the new ratio becomes 40:57. What is Sumit present salary.

32000
34000
38000
40000

Answer: Option C

Explanation:

Let the original Salaries of Ravi and Sumit is 2x and 3x.

So as per question

\begin{aligned}
\frac{2x+4000}{3x+4000} = \frac{40}{57} \\
=> 57(2x+4000) = 40(3x+4000) \\
=> 6x = 68000 \\
=> 3x = 34000 \\

\text{ Sumit Salary =} 3x+4000 \\
34000 + 4000 = 38000

\end{aligned}