# Chain Rule Questions

**FACTS AND FORMULAE FOR CHAIN RULE QUESTIONS**

**1. Direct Proportion: **Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent.

Ex. 1. Cost is directly proportional to the number of articles. (More Articles, More Cost)

Ex. 2. Work done is directly proportional to the number of men working on it (More Men, More Work)

**2. Indirect Proportion: **Two quantities are said to be indirectly proportional,if on the increase of the one, the other decreases to the same extent and vice-versa.

Ex. 1. The time taken by a car in covering a certain distance is inversely proportional to the speed of the car. (More speed, Less is the time taken to cover a distance)

Ex. 2. Time taken to finish a work is inversely proportional to the num of persons working at it. (More persons, Less is the time taken to finish a job)

A) 75 | B) 82 |

C) 100 | D) 110 |

Explanation:

Originally let there be x men.

Less men, More days (Indirect Proportion)

(x-10) : x :: 100 :110 10x= 1100 x= 110

A) 46 | B) 47 |

C) 48 | D) 49 |

Explanation:

Let the required length be x meters

More men, More length built (Direct proportion)

Less days, Less length built (Direct Proportion)

(20 x 6 x X)=(35 x 3 x 56)

Hence, the required length is 49 m.

A) 18 days | B) 21 days |

C) 24 days | D) 30 days |

Explanation:

5 men= 10 boys 1man= 2 boys

(2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys

( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys.

Let the required number of days be x.

More boys , Less days (Indirect proportion)

More work , More days (Direct proportion)

Hence, the required number of days = 21

A) 1 | B) 3 |

C) 7 | D) 14 |

Explanation:

Let the required number days be *x*.

*Less spiders, More days (Indirect Proportion)*

*Less webs, Less days (Direct Proportion)*

1 x 7 x *x* = 7 x 1 x 7

=> x= 7

A) 9 | B) 10 |

C) 11 | D) 12 |

Explanation:

Let the required no of working hours per day be x.

More pumps , Less working hours per day (Indirect Proportion)

Less days, More working hours per day (Indirect Proportion)

X= x=12