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Ratio
Question 211 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Of three positive numbers, the ratio of first and second is 8 : 9, that of second and third is 3 : 4. The product of first and third is 2400. The sum of the three number is =?
155 | |
295 | |
185 | |
145 |
Question 211 Explanation:
\begin{align} & {\text{First}}:{\text{Second}}:{\text{Third}} \cr & \, \, \, \, 8\, \, \, \, \, \, :\, \, \, \, \, \, 9 \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, 3\, \, \, \, \, \, \, \, \, \, \, :\, \, \, \, \, 4 \cr & \frac{{\overline {\, \, \, 24\, \, \, :\, \, \, \, \, 27\, \, \, \, \, \, \, \, :\, \, \, \, 36} }}{{\underline {\, 8\, \, \, \, \, \, \, \, :\, \, \, \, \, \, \, \, 9\, \, \, \, \, \, \, \, :\, \, \, \, 12} }} \cr & {\text{Let 8x}}:{\text{9x}}:{\text{12x}} \cr & \therefore {\text{First}} \times {\text{Third}} \cr & 8x \times 12x = 2400 \cr & \Rightarrow 96{x^2} = 2400 \cr & \Rightarrow {x^2} = \frac{{2400}}{{96}} = 25 \cr & \Rightarrow x = 5 \cr & \therefore {\text{Sum of three numbers }} \cr & {\text{First}} + {\text{Second}} + {\text{Third}} \cr & 8x + 9x + 12x = 29x \cr & \therefore 29 \times 5 = 145 \cr\end{align}
Question 212 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
The ratio of the incomes of Ram and Shyam is 7 : 17 and that of Shyam and Sohan is 7 : 17. If the income of Ram is Rs. 490, what is the income of Sohan?
Rs. 2790 | |
Rs. 2890 | |
Rs. 490 | |
Rs. 1190 |
Question 212 Explanation:
\begin{align} & {\text{Ram}}:{\text{Shyam}} = 7:17 \cr & {\text{Shyam}}:{\text{Sohan}} = 7:17 \cr & = \left( {7 \times \frac{{17}}{7}} \right):\left( {17 \times \frac{{17}}{7}} \right) \cr & = 17:\frac{{289}}{7}. \cr & {\text{Ram}}:{\text{Shyam}}:{\text{Sohan}} \cr & = 7:17:\frac{{289}}{7} \cr & = 49:119:289. \cr\end{align} Let Sohan's income be Rs. x
Then,
= 49 : 289 :: 490 : x or x = 2890
Question 213 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
Which of the following represents ab = 64?
a : 8 = b : 8 | |
32 : a = b : 2 | |
8 : a = 8 : b | |
a : 16 = 6 : 4 |
Question 213 Explanation:
A = 8 : a = 8 : b ⇒ 8a = 8b ⇒ a = b.
B = a : 16 = 6 : 4 ⇒ 4a = 16b ⇒ a = 4b
C = a : 8 = b : 8 ⇒ 8a = 8b ⇒ b = a D = 32 : a = b : 2 ⇒ ab =64
There are 213 questions to complete.