# 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) 29.32 sec | B) 42.51 sec |

C) 39.25 sec | D) 45.61 sec |

Explanation:

Given loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in,

1.14 ----- 1

52.0 ------?

$\Rightarrow \frac{52}{1.14}$= 45.61 sec

A) Rs. 175 | B) Rs. 325 |

C) Rs. 340 | D) Rs. 260 |

Explanation:

Assume first child (the youngest) get = Rs. x

According to the question ;

each son having Rs. 30 more than the younger one

Second child will get = Rs. x + 30

Third child will get = Rs. x + 30 + 30 = x + 60

Forth child will get = Rs. x + 30 + 30 + 30 = x + 90

Fifth child will get = Rs. x + 30 + 30 + 30 + 30 = x + 120

Total amount they got = Rs. 2000

x + (x+30) + (x+60) + (x+90) + (x+120) = 2000

5x + 300 = 2000

5x = 1700

x = Rs. 340

So the youngest child will get Rs. 340.

A) 144 | B) 148 |

C) 156 | D) 186 |

Explanation:

Less toys, Less Price (Direct Proportion)

So, let the price be Rs. x

then,

23:12::276:x => x=(276*12)/23

=> x=144

So price of 12 toys will be Rs. 144

A) 78 paise | B) 48 paise |

C) 54 paise | D) 62 paise |

Explanation:

Quarter of Kg means 250 gm

Less weight, less price (Direct Proportion)

So,

250 : 200 :: 60 : x => x = 48

So 200 gm will cost 48 paise.

A) 46 | B) 32 |

C) 35 | D) 30 |

Explanation:

(Men 14 : 16) : (Hrs/Day 12 : 7) :: 48 : x

14 * 12 * x = 16 * 7 * 48 or x = 32

A) 18 | B) 14 |

C) 22 | D) 24 |

Explanation:

1 2 3 4 5 6(Shankar) 7(Nitu) 8(Althaf) 9 10 11 12 13 14

Here, Althaf is 8th from front, Shankar is 9th from rear end and Nitu is between them

So minimum no. of boys standing in the queue = 14