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Ratio
Question 1 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
5 : 3 | |
3 : 7 | |
7 : 3 | |
2 : 5 |
Question 1 Explanation:
\begin{align} & {\text{Let}}\, 40\% \, {\text{of}}\, A = \frac{2}{3}B \cr & {\text{Then}}, \, \frac{{40A}}{{100}} = \frac{{2B}}{3} \cr & \Rightarrow \frac{{2A}}{5} = \frac{{2B}}{3} \cr & \Rightarrow \frac{A}{B} = \left( {\frac{2}{3} \times \frac{5}{2}} \right) = \frac{5}{3} \cr & \therefore A:B = 5:3. \cr\end{align}
Question 2 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Which of the following represents a correct proportion?
3 : 5 :: 2 : 5 | |
13 : 11 ::5 : 4 | |
30 : 45 ::13 : 24 | |
12 : 9 ::16 : 12 |
Question 2 Explanation:
a : b :: c : d
a $\times$ d = b $\times$ c
So, go through options
(A). 9 $\times$ 16 = 12 $\times$ 12 (right)
(B). 13 $\times$ 4 = 11 $\times$ 5 (wrong)
(C). 30 $\times$ 24 = 45 $\times$ 13 (wrong)
(D). 3 $\times$ 5 = 5 $\times$ 2 (wrong)
So answer is 12 : 9 :: 16 : 12
Question 3 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
30 | |
58 | |
20 | |
48 |
Question 3 Explanation:
Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 \begin{align} & = \left( {5 \times \frac{3}{5}} \right):\left( {8 \times \frac{3}{5}} \right) = 3:\frac{{24}}{5} \cr & \Rightarrow A:B:C = 2:3:\frac{{24}}{5} = 10:15:24 \cr & \Rightarrow B = \left( {98 \times \frac{{15}}{{49}}} \right) = 30. \cr\end{align}
Question 4 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
If A:B = 2:3, B:C = 4:5 and C:D = 5:9 then A:D is equal to:
2:9 | |
8:27 | |
11:17 | |
5:9 |
Question 4 Explanation:
\begin{align} & \frac{A}{D} = \left( {\frac{A}{B}} \right) \times \left( {B \times C} \right) \times \left( {\frac{C}{D}} \right) \cr & \, \, \, \, \, \, \, \, \, = \left( {\frac{2}{3}} \right) \times \left( {\frac{4}{5}} \right) \times \left( {\frac{5}{9}} \right) \cr & \, \, \, \, \, \, \, \, \, = \frac{{\left( {2 \times 4 \times 5} \right)}}{{\left( {3 \times 5 \times 9} \right)}} \cr & \, \, \, \, \, \, \, \, \, = \frac{8}{{27}} \cr & \, \, \, \, \, \, \, \, \, = 8:27 \cr\end{align}
Question 5 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
The ratio of age of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be =?
17/18 | |
22/24 | |
15/16 | |
11/12 |
Question 5 Explanation:
Ratio of ages of Boys A and B \begin{align} & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, {\text{A}}:{\text{B}} \cr & {\text{Present age }}5x:6x \cr & \therefore {\text{After two years }} \cr & \therefore \frac{{5x + 2}}{{6x + 2}} = \frac{7}{8} \cr & \Rightarrow 40x + 16 = 42x + 14 \cr & \Rightarrow 2x = 2 \cr & \Rightarrow x = 1 \cr & \therefore {\text{Present age }} \cr & {\text{A}} = 5 \times 1 = 5 \cr & {\text{B}} = 6 \times 1 = 6 \cr & {\text{After 12 years}} \cr & {\text{A}} = 5 + 12 = 17 \cr & {\text{B}} = 6 + 12 = 18 \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{{17}}{{18}} \cr\end{align}
There are 5 questions to complete.