Aptitude ratio MCQ

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Ratio

Question 36 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
A
49
B
27
C
55
D
33
Question 36 Explanation: 
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{number}}\, {\text{be}}\, 3x\, {\text{and}}\, 5x. \cr & {\text{Then}}, \, \frac{{3x - 9}}{{5x - 9}} = \frac{{12}}{{23}} \cr & \Rightarrow 23\left( {3x - 9} \right) = 12\left( {5x - 9} \right) \cr & \Rightarrow 9x = 99 \cr & \Rightarrow x = 11. \cr & \therefore {\text{The}}\, {\text{smaller}}\, {\text{number}} \cr & = \left( {3 \times 11} \right) \cr & = 33 \cr\end{align}
Question 37 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
The income of A, B and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves 1/4 th of his income then the savings of A, B and C are in the ratio of =?
A
69 : 56 : 99
B
99 : 56 : 69
C
56 : 99 : 69
D
99 : 69 : 56
Question 37 Explanation: 
Let income of A, B and C are 7x, 9x and 12x respectively

and expenditure of A, B and C are 8y, 9y and 15y respectively \begin{align} & \Rightarrow {\text{ Income of, }} \cr & A \times \frac{1}{4}{\text{ = Saving of A (given)}} \cr & \Rightarrow 7x - 8y = 7x \times \frac{1}{4} \cr & \Rightarrow 28x - 32y = 7x \cr & \Rightarrow 21x = 32y \cr & \Rightarrow x:y = 32:21 \cr\end{align} ∴ The ratio of savings of A, B and C

⇒ (7x - 8y) : (9x - 9y) : (12x : 15y)

⇒ (7 $\times$ 32 - 8 $\times$ 21) : (9 $\times$ 32 - 9 $\times$ 21) : (12 $\times$ 32 - 15 $\times$ 21)

⇒ (224 - 168) : (288 - 189) : (384 - 315) ⇒ 56 : 99 : 69

Question 38 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Brindavan Express leave Chennai Central Station every day at 07.50 am and goes to Bangalore City Railway station. This train is very popular among the travelers. On 25th July 2012 number of passengers traveling by I class and II class was in the ratio 1:4. The fare for this travel is in the ratio 3:1. The total fare collected was Rs. 224000/. (Rs. Two lakhs twenty four thousand only). What was the fare collected from I class passengers on that day?
A
Rs. 5, 00, 000
B
Rs. 96000
C
Rs.128000
D
Rs.32000
Question 38 Explanation: 
Let the number of passenger traveling by first class be x.

Then, number of passenger traveling by second class will be 4x.

But the fare is in the ratio 3:1

In other words, if 3y fare is collected per I class passenger, y would be collected per II class passenger.

Fares of I class passengers : Fares of II class passengers

= x*3y : 4x*y

= 3:4 The above ratio can be interpreted as follows.

If total fare is 3+4 = 7, then I class passengers should pay Rs. 3

Similarly, we can calculate the fare of I class passengers when total was 224000

Total Fare I Class Fare

7 3

224000?

= 224000*(3/7) = Rs. 96000.

Question 39 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
If a : b = 3 : 4, b : c = 4 : 7, then $\frac{{a + b + c}}{c}{\text{ is equal to - }}$
A
3
B
7
C
1
D
2
Question 39 Explanation: 
\begin{align} & = a:b = 3:4 \cr & = b:c = 4:7 \cr & \Rightarrow a:b:c = 3:4:7 \cr & {\text{Let }}a = 3k, \cr & \, \, \, \, \, \, \, \, \, \, b = 4k, \cr & \, \, \, \, \, \, \, \, \, \, c = 7k. \cr & {\text{Then, }} \cr & \frac{{a + b + c}}{c} \cr & = \frac{{3k + 4k + 7k}}{{7k}} \cr & = \frac{{14k}}{{7k}} \cr & = 2. \cr\end{align}
Question 40 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A vessel of capacity 2 litre has 25% alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. what is the new concentration of mixture?
A
71%
B
29%
C
49%
D
31%
Question 40 Explanation: 
Amount of alcohol in first vessel,

= 25% of 2 litre

= 0.25*2 = 0.5 litre

Amount of alcohol in second vessel,

= 40% of 6 litre

= 0.4*6 = 2.4 litre

Total amount of alcohol out of 10 litres of mixture is,

0.5+2.4 = 2.9 litre.

Thus, Concentration of the mixture is,

(2.9*100)/10

= 29%.

There are 40 questions to complete.

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