Arithmetic: Ratio and Proportion Test-4

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Arithmetic: Ratio and Proportion Test-4

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Question 1

The ages of Sulekha and Arunima are in the ratio of 9: 8 respectively. After 5 years the ratio of their ages will be 10: 9. What is the difference in years between their ages.

A	4 years
B	5 years
C	6 years
D	7 years

Question 1 Explanation:

Let the common ratio be x
So,present age of Sulekha=9x
Present age of Arunima=8x
Also(9x+5)/(8x+5)=10/9
x=5
Difference between their ages=x=5

Question 2

The largest and the second largest angles of a triangle are in the ratio of 13 : 12 respectively. The smallest angle is 20% of the sum of the largest and the second largest angles. What is the sum of the smallest and the second largest angles?

A	120
B	108
C	100
D	102

Question 2 Explanation:

Let the common ratio of largest and second largest angles be x
Largest angle=13x
Second largest angle=12x
Smallest angle=(20/100)×25x=5x
So,13x+12x+5x=180
x=6
Sum=17x=102

Question 3

Two numbers are such as the square of one is 224 less than 8 times the square of the other. If the numbers be in the ratio of 3: 4 their values are

A	12, 16
B	6, 8
C	9, 12
D	None of these

Question 3 Explanation:

Let the common ratio of the numbers be x
The 2 numbers are 3x and 4x
$ \begin{array}{l}16{{x}^{2}}=8\times
9{{x}^{2}}-224\\x=2\\so\,\,the\,\,numbers\,are\,\,6\,and\,8\end{array}$

Question 4

Railway fares of 1st, 2nd and 3rd classes between two stations were in the ratio of 8 : 6 : 3. The fares of 1st and 2nd class were subsequently reduced by 1/6 and 1/12, respectively. If during a year, the ratio between the passengers of 1st, 2nd and 3rd classes was 9: 12: 26 and total amount collected by the sale of tickets was Rs.1088, then find the collection from the passengers of 1st class.

A	Rs.260
B	Rs.280
C	Rs.300
D	Rs.320

Question 4 Explanation:

Let the ratio of original fares be p
Orignal fare of 1st class=8p
Orignal fare of 2nd class=6p
Orignal fare of 3rd class=3p
Revised fares of 1st class=5/6×8p=20/3p
Revised fares of 2nd class=11/12×6p=11/2p
Let the ratio of passengers be y
Passengers travelled in 1st class=9y
Passengers travelled in 2nd class=12y
Passengers travelled in 3rd class=26y
Total collection,20/3x×9y+11/2p×12y+3p×26y=1088
py=1088/204
60py=320

Question 5

At Narmada Sarovar Bachao (NSB) demonstration, supporters of Ms Patkar outnumbered the police by 9: 1. The police arrested 135 NSB supporters averaging 5 for every 3 policemen. How many supporters of NSB were there in the demonstration