# 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) 16 | B) 12 |

C) 8 | D) 4 |

Explanation:

Let the required number of bottles be *x*.

*More weavers, More mats (Direct Proportion)*

*More days, More mats (Direct Proportion)*

$weavers4:8\}:4:x\phantom{\rule{0ex}{0ex}}days4:8\}:4:x$

4 x 4 x *x* = 8 x 8 x 4

=> x = $\frac{8*8*4}{4*4}$

*=> x* = 16.

A) 29 | B) 37 |

C) 42 | D) 54 |

Explanation:

After 10 days : 150 men had food for 35 days.

Suppose 125 men had food for *x* days.

Now, *Less men, More days (Indirect Proportion)*

$\therefore $ 125 : 150 **::** 35 : *x* $\iff $ 125 x *x* = 150 x 35

$\Rightarrow x=\frac{150\times 35}{125}=42$

A) 194 seconds | B) 195 seconds |

C) 196 seconds | D) 197seconds |

Explanation:

Let the time required by x seconds.

Then, More cloth means More time (Direct Proportion)

So, 0.128 : 1 :: 25 : x

$\Rightarrow x=\frac{1\times 25}{0.128}$ => x = 195.31

So time will be approx 195 seconds

A) 14th element | B) 9th element |

C) 12th element | D) 7th element |

Explanation:

If we consider the third term to be ‘x”

The 15th term will be (x + 12d)

6th term will be (x + 3d)

11th term will be (x + 8d) and

13th term will be (x + 10d).

Thus, as per the given condition, 2x + 12d = 3x + 21d.Or x + 9d = 0.

x + 9d will be the 12th term.

Thus, 12th term of the A.P will be zero.

A) 50 | B) 40 |

C) 30 | D) 20 |

Explanation:

There is a meal for 200 children. 150 children have taken the meal.

Remaining meal is to be catered to 50 children.

Now, 200 children = 120 men.

50 children = $\left(\frac{120}{200}\right)50$ =30men

A) 648 | B) 1800 |

C) 2700 | D) 10800 |

Explanation:

Let the required number of bottles be *x*.

*More machines, More bottles (Direct Proportion)*

*More minutes, More bottles (Direct Proportion)*

$\left.\begin{array}{r}\begin{array}{cc}machines& 6:10\end{array}\\ \begin{array}{cc}time(inmin)& 1:4\end{array}\end{array}\right\}\vdots \vdots 270:x$

=> 6 * 1 * *x* = 10 * 4 * 270

=> x= 1800

A) 4 hours a day | B) 5 hours a day |

C) 6 hours a day | D) 7 hours a day |

Explanation:

More Men, Less Hours {Indirect Proportion}

Less Days, More Hours {Indirect Proportion}

$\left.\begin{array}{r}\begin{array}{cc}men& 15:10\end{array}\\ \begin{array}{cc}days& 12:18\end{array}\end{array}\right\}\vdots \vdots 6:x$

=> 15 * 12 * x = 10 * 18 * 6

=>x = 6

A) Rs.120 | B) Rs.100 |

C) Rs.200 | D) Rs.220 |

Explanation:

Let the required Price be Rs. X .Then, Lest toys , Less cost (Direct Proportion)

Therefore 6 : 5 :: 264.37 : x

=> 6 * x = 5 * 264.37

=> X= 220.308

Therefore, Approximate price of 5 toys = Rs. 220