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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.

4 years | |

5 years | |

6 years | |

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

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?

120 | |

108 | |

100 | |

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

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

12, 16 | |

6, 8 | |

9, 12 | |

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}$

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.

Rs.260 | |

Rs.280 | |

Rs.300 | |

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

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

1215 | |

665 | |

405 | |

None of these |

Question 5 Explanation:

Total arrested = 135

Number of policeman =3x=81

So total number of supporters=729

Number of policeman =3x=81

So total number of supporters=729

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