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Ratio
Question 61 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
The sum of three numbers is 116. The second number and the third number are in the ratio of 9 : 16 while the first number and the third number are in the ratio of 1 : 4. Find the second number.
8 | |
64 | |
None of these | |
16 |
Question 61 Explanation:
\begin{align} & {\text{Second}}:{\text{Third}} \cr & = {\text{9}}:{\text{16, }} \cr & {\text{Third}}:{\text{first}} \cr & = {\text{4}}:{\text{1}} \cr & {\text{ = 16}}:{\text{4}}{\text{.}} \cr & \therefore {\text{Second}}:{\text{Third}}:{\text{first}} \cr & = {\text{9}}:{\text{16}}:{\text{4}}{\text{.}} \cr & {\text{Second number}} \cr & = \left( {{\text{116}} \times \frac{{\text{9}}}{{{\text{29}}}}} \right) \cr & = {\text{36}} \cr\end{align}
Question 62 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
If A : B : C = 2 : 3 : 4, then the ratio $\frac{{\text{A}}}{{\text{B}}}{\text{:}}\frac{{\text{B}}}{{\text{C}}}{\text{:}}\frac{{\text{C}}}{{\text{A}}}{\text{ is equal to - }}$
8 : 9 : 16 | |
8 : 9 : 12 | |
8 : 9 : 24 | |
4 : 9 : 16 |
Question 62 Explanation:
\begin{align} & {\text{let A}} = 2{\text{k}}, \cr & {\text{B}} = 3{\text{k}} \cr & {\text{C}} = 4{\text{k}}. \cr & {\text{Then, }} \cr & \Rightarrow \frac{{\text{A}}}{{\text{B}}} = \frac{{2{\text{k}}}}{{3{\text{k}}}} = \frac{2}{3}, \cr & \Rightarrow \frac{{\text{B}}}{{\text{C}}} = \frac{{3{\text{k}}}}{{4{\text{k}}}} = \frac{3}{4}, \cr & \Rightarrow \frac{{\text{C}}}{{\text{A}}} = \frac{{4{\text{k}}}}{{2{\text{k}}}} = 2. \cr & \Rightarrow \frac{{\text{A}}}{{\text{B}}}:\frac{{\text{B}}}{{\text{C}}}:\frac{{\text{C}}}{{\text{A}}} = \frac{2}{3}:\frac{3}{4}:2 \cr & = 8:9:24. \cr\end{align}
Question 63 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
The sum of the squares of three numbers is 532 and the ratio of the first and the second as also of the second and the third is 3 : 2. The third number is -
18 | |
20 | |
8 | |
12 |
Question 63 Explanation:
\begin{align} & {\text{First}}:{\text{Second}} = 3:2, \cr & {\text{Second}}:{\text{Third}} = 3:2 \cr & = \left( {3 \times \frac{2}{3}} \right):\left( {2 \times \frac{2}{3}} \right) \cr & = 2:\frac{4}{3}. \cr & \therefore {\text{Ratio between the numbers}} \cr & = 3:2:\frac{4}{3} \cr & = 9:6:4. \cr\end{align} Let the numbers be 9x, 6x and 4x
Then,
= (9x)2 + (6x)2 + (4x)2 = 532
⇒ 81x2 + 36x2 + 16x2 = 532
⇒ 133x2 = 532
⇒ x2 = 4
⇒ x = 2 So, third number = 4x = 4 $\times$ 2 = 8
Question 64 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
If p : q = 3 : 4, r : s = 8 : 5 and x : y = 10 : 6, then psx : qry is equal to.
16/25 | |
75/32 | |
25/32 | |
2 |
Question 64 Explanation:
\begin{align} & = \frac{p}{q} = \frac{3}{4}, \frac{r}{s} = \frac{8}{5}, \frac{x}{y} = \frac{{10}}{6} \cr & \Rightarrow p = \frac{{3q}}{4}, r = \frac{{8s}}{5}, x = \frac{{5y}}{3}. \cr & \therefore \frac{{psx}}{{qry}} = \frac{{\frac{{3q}}{4} \times s \times \frac{{5y}}{3}}}{{q \times \frac{{8s}}{5} \times y}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{{\frac{5}{4}qsy}}{{\frac{8}{5}qsy}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{5}{4} \times \frac{5}{8} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{{25}}{{32}}. \cr\end{align}
Question 65 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
\begin{align} & {\text{If A}}:{\text{B}} = \frac{1}{2}:\frac{3}{8}{\text{, }} \cr & {\text{B}}:{\text{C}} = \frac{1}{3}:\frac{5}{9}{\text{ and}} \cr & {\text{C}}:{\text{D}} = \frac{5}{6}:\frac{3}{4}{\text{, }} \cr\end{align} Then the ratio of A : B : C 😀 is?
6 : 4 : 8 : 10 | |
6 : 8 : 9 : 10 | |
8 : 6 : 10 : 9 | |
4 : 6 : 8 : 10 |
Question 65 Explanation:
\begin{align} & {\text{A}}:{\text{B}} = \frac{1}{2}:\frac{3}{8}, \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{4}{3} \cr & {\text{B}}:{\text{C}} = \frac{1}{3}:\frac{5}{9}, \cr & \frac{{\text{B}}}{{\text{C}}} = \frac{1}{3} \times \frac{9}{5} = \frac{3}{5} \cr & {\text{C}}:{\text{D}} = \frac{5}{6}:\frac{3}{4}, \cr & \frac{{\text{C}}}{{\text{D}}} = \frac{{5 \times 4}}{{6 \times 3}} = \frac{{10}}{9} \cr & {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & {\text{4}}:{\text{3}} \cr & \, \, \, \, \, \, \, {\text{3}}:{\text{5}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, {\text{ 10}}:{\text{9}} \cr & \Rightarrow {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & \, \, \, \, \, \, \, \, \, 8:6:10:9 \cr\end{align}
There are 65 questions to complete.