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Ratio
Question 96 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
The ratio of 252.5 : 53 is same as =?
1 : 25 | |
5 : 3 | |
25 : 1 | |
5 : 6 |
Question 96 Explanation:
\begin{align} & \, \, \, \, \, \, \, {25^{2.5}}:{5^{3{\text{ }}}} \cr & {(5)^{2.5 \times 2}}:{5^{3{\text{ }}}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, {5^5}:{5^3} \cr & \, \, \, \, \, \, {5^3}{.5^2}:{5^{3{\text{ }}}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, {5^2}:1 \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, 25:1 \cr\end{align}
Question 97 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
If x : y = 3 : 1, then x3 - y3 : x3 + y3 =?
14 : 13 | |
11 : 10 | |
10 : 11 | |
13 : 14 |
Question 97 Explanation:
\begin{align} & x:y = 3:1 \cr & \therefore \frac{x}{y} = \frac{3}{1} \cr & \therefore \frac{{{x^3} - {y^3}}}{{{x^3} + {y^3}}} \cr & \Rightarrow \frac{{{y^3}\left( {\frac{{{x^3}}}{{{y^3}}} - 1} \right)}}{{{y^3}\left( {\frac{{{x^3}}}{{{y^3}}} + 1} \right)}} \cr & {\text{taking }}{{\text{y}}^3}{\text{ common}} \cr & {\text{ = }}\frac{{\frac{{{x^3}}}{{{y^3}}} - 1}}{{\frac{{{x^3}}}{{{y^3}}} + 1}} \cr & \Rightarrow \frac{{27 - 1}}{{27 + 1}} \cr & \Rightarrow \frac{{26}}{{28}} \cr & \Rightarrow \frac{{13}}{{14}} \cr\end{align}
Question 98 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Two numbers are in ratio 7:11. If 7 is added to each of the numbers, the ratio becomes 2:3. The smaller number is
77 | |
39 | |
66 | |
49 |
Question 98 Explanation:
Let the numbers be 7x and 11x.
\begin{align} & {\text{According to question}}, \cr & \frac{{\left( {7x + 7} \right)}}{{\left( {11x + 7} \right)}} = \frac{2}{3} \cr & Or, \, 22x + 14 = 21x + 21 \cr & Or, \, x = 7 \cr & {\text{Smaller}}\, {\text{number}} = 49 \cr\end{align}
Question 99 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A, B, C and D have Rs. 40, Rs. 50, Rs. 60 and Rs. 70 respectively when they go to visit a fair. A spends Rs. 18, B spends Rs. 21, C spends Rs. 24 and D spends Rs. 27. Who has done the highest expenditure proportionate to his resources?
B | |
D | |
A | |
C |
Question 99 Explanation:
Ratio of the expenditures of A, B, C, D are as under: \begin{align} & {\text{A}} \to \frac{{18}}{{40}} = \frac{9}{{20}} = 0.45 \cr & {\text{B}} \to \frac{{21}}{{50}} = 0.42 \cr & {\text{C}} \to \frac{{24}}{{60}} = 0.4 \cr & {\text{D}} \to \frac{{27}}{7} = 0.385. \cr\end{align} ${\text{Clearly, A has done the highest expenditure proportionate to his resources}}{\text{.}}$
Question 100 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
If a : b = 2 : 3 and b : c = 4 : 5, then (a + b) : (b + c) is equal to-
6 : 8 | |
8 : 6 | |
20 : 27 | |
27 : 20 |
Question 100 Explanation:
\begin{align} & {\text{a}}:{\text{b}} = {\text{2}}:{\text{3}}, \cr & {\text{b}}:{\text{c}} = {\text{4}}:{\text{5}} = {\text{4}} \times \frac{3}{4}:5 \times \frac{3}{4} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 3:\frac{{15}}{4}. \cr & So, a:b:c = 2:3:\frac{{15}}{4} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 8:12:15. \cr & {\text{Let}} \cr & {\text{a}} = 8{\text{k}}, \cr & {\text{b}} = 12{\text{k}}, \cr & {\text{c}} = 15{\text{k}}. \cr & {\text{Then, }} \cr & \frac{{\left( {{\text{a}} + {\text{b}}} \right)}}{{\left( {{\text{b}} + {\text{c}}} \right)}} = \frac{{\left( {8{\text{k}} + 12{\text{k}}} \right)}}{{\left( {12{\text{k}} + 15{\text{k}}} \right)}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{{20{\text{k}}}}{{27{\text{k}}}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \frac{{20}}{{27}}. \cr\end{align}
There are 100 questions to complete.