### Exercise :: Arithmetic Reasoning - Section 1

- Arithmetic Reasoning - Section 1
- Arithmetic Reasoning - Section 2

16. | In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ? |
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Answer: Option C Explanation: Let the number of boys and girls participating in sports be 3x and 2x respectively. Then, 3x = 15 or x = 5. So, number of girls participating in sports = 2x = 10. Number of students not participating in sports = 60 - (15 + 10) = 35. Let number of boys not participating in sports be y. Then, number of girls not participating in sports = (35 -y). Therefore (35 - y) = y + 5 2y 30 y = 15. So, number of girls not participating in sports = (35 - 15) = 20. Hence, total number of girls in the class = (10 + 20) = 30. |

17. | There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there ? |
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Answer: Option D Explanation: Let x and y be the number of deer and peacocks in the zoo respectively. Then, x + y = 80 ...(i) and 4x + 2y = 200 or 2x + y = 100 ...(ii) Solving (i) and (ii), we get) x = 20, y = 60. |

18. | A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair ? |
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Answer: Option A Explanation: Since there are socks of only two colours, so two out of any three socks must always be of the same colour. |

19. | A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ? |
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Answer: Option D Explanation: Total number of routes from Bristol to Carlisle = (4 x 3 x 2) = 24. |

20. | Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win ? |
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Answer: Option C Explanation: Let money with Ken = x. Then, money with Mac = x + £ 3. Now, 3x = (x + x + £ 3) + £ 2 x = £ 5. Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13. |