# 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) 40 | B) 50 |

C) 60 | D) 70 |

Explanation:

Let the required no of hours be x. Then

Less men , More hours (Indirct Proportion)

Therefore, 15:36 ::25:x

=> (15 x X)=(36 x 25) => x = 60

Hence, 15 men can do it in 60 hours.

A) 4 | B) 9 |

C) 12 | D) 49 |

Explanation:

Let the required number of revolutions made by larger wheel be *x*.

Then, *More cogs, Less revolutions (Indirect Proportion)*

* *14 : 6 **::** 21 : *x =>** 14 x x = 6 x 21*

*x=6*21/14 => x=9*

A) 6 days | B) 12 days |

C) 4 days | D) 3 days |

Explanation:

Let x men can do the in 12 days and the required number of days be z

More men, Less days [Indirect Proportion]

Less work, Less days [Direct Proportion ]

$\left.\begin{array}{r}\begin{array}{cccc}men& 2x& :& x\end{array}\\ \begin{array}{cccc}work& 1& :& \frac{1}{2}\end{array}\end{array}\right\}::12:z$

$\therefore \left(2x\times 1\times z\right)=\left(x\times \frac{1}{2}\times 12\right)$

$\Rightarrow z=3$

A) Rs. (xy/d) | B) Rs. (xd) |

C) Rs. (yd) | D) Rs. (yd/x) |

Explanation:

Cost of x metres = Rs. d.

Cost of 1 metre = Rs.(d/x)

Cost of y metres = Rs.[(d/x).y] = Rs.(yd/x)

A) 48 Paise | B) 54 Paise |

C) 56 Paise | D) 72 Paise |

Explanation:

Let the Required cost be X paise. Less Weight , Less cost (Direct Proportion)

Therefore, 250 : 200 :: 60 : x

=> (250 * x) = (200 * 60)

=> x= 48

A) 22 | B) 14 |

C) 13 | D) 11 |

Explanation:

Let the required no of binders be X.

Less books , Less binders (Direct Proportion)

More days, Less binders (Indirect proportion)

$\left.\begin{array}{r}\begin{array}{cc}Books& 900:660\end{array}\\ \begin{array}{cc}Days& 12:10\end{array}\end{array}\right\}\vdots \vdots 18:x$

Therefore, (900 * 12 * x) = (660 * 10 * 18)

=> x = 11

A) 350 | B) 400 |

C) 425 | D) 450 |

Explanation:

Let the required no of hectares be x. Then

More men, More hectares (Direct proportion)

More days, More hectares (Direct proportion)

$\left.\begin{array}{r}\begin{array}{cc}Men& 8:36\end{array}\\ \begin{array}{cc}Days& 24:30\end{array}\end{array}\right\}\vdots \vdots 80:x$

=> ( 8 * 24 * x) = (36 * 30 * 80)

=> x= 450

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.