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This module will teach you the basics of direct and indirect proportions. These concepts will further help you in time and work questions.

**Important Formulas â€“ chain rule**

**Direct Proportion**

Two quantities are said to be directly proportional, if on the increase or decrease of the one, the other increases or decreases the same extent.

**Examples**

- Cost of the goods is directly proportional to the number of goods. (More goods, More cost)
- Amount of work done is directly proportional to the number of persons who did the work. (More persons, More Work)

**Indirect Proportion (inverse proportion)**

Two quantities are said to be indirectly proportional (inversely proportional) if on the increase of the one, the other decreases to the same extent and vice-versa.**Examples**

- Number of days needed to complete a work is indirectly proportional (inversely proportional) with the number of persons who does the work (More Persons, Less Days needed)
- The time taken to travel a distance is indirectly proportional (inversely proportional) with the speed in which one is travelling (More Speed, Less Time)

__Solved Examples__

1. If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate? | |

A. Rs. (xd/y) | B. Rs. x/d |

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

**Answer :** Option C

**Explanation** **:**

cost of x metres of wire = Rs. d

cost of 1 metre of wire = Rs.(d/x)

cost of y metre of wire = Rs.(yÃ—d/x)=Rs. (yd/x)

2. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal? | |

A. 50 | B. 30 |

C. 40 | D. 10 |

**Answer** **:** Option B

**Explanation** **:**

Meal for 200 children = Meal for 120 men

Meal for 1 child = Meal for 120/200 men

Meal for 150 children = Meal for (120Ã—150)/200 men=Meal for 90 men

Total mean available = Meal for 120 men

Renaming meal = Meal for 120 men - Meal for 90 men = Meal for 30 men

3. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? | |

A. 26 | B. 22 |

C. 12 | D. 24 |

**Answer :** Option D

**Explanation :**

Let the required number of days be x

More men, less days (indirect proportion)

Hence we can write as

Men36:27}::x:18 â‡’36Ã—18=27Ã—x â‡’12Ã—18=9Ã—x

â‡’12Ã—2=x

â‡’x=24

| |

A. 15 | B. 12 |

C. 21 | D. 9 |

**Answer :** Option D

**Explanation :**

Let the number of revolutions made by the larger wheel be x

More cogs, less revolutions (Indirect proportion)

Hence we can write as

Cogs 6:14}: x: 21 â‡’6Ã—21=14Ã—x â‡’6Ã—3=2Ã—x â‡’3Ã—3=x â‡’x=9

5. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day? | |

A. 10 | B. 12 |

C. 8 | D. 15 |

**Answer :** Option B

**Explanation :**

Let the required hours needed be x

More pumps, less hours (Indirect proportion)

More Days, less hours (Indirect proportion)

Hence we can write as

â‡’3*Ã—**2*Ã—8=4Ã—1Ã—x

â‡’3Ã—2Ã—2=x

â‡’x=12

6. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? | |

A. 9 | B. 12 |

C. 10 | D. 13 |

**Answer :** Option D

**Explanation :**

Let the required number of days be x

More hours, less days (indirect proportion)

Hence we can write as

â‡’39Ã—5Ã—12=30Ã—6Ã—x â‡’39Ã—5Ã—2=30Ã—x â‡’39=3Ã—x â‡’x=13

7. A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth? | |

A. 205 | B. 200 |

C. 180 | D. 195 |

**Answer : **Option D

**Explanation :**

Let the required number of seconds be x

More cloth, More time, (direct proportion)

Hence we can write as

Cloth 0.128:25} :: 1:x

â‡’0.128x=25 â‡’x=25/0.128 â‡’25000/128=3125/16â‰ˆ195

8. 21 goats eat as much as 15 cows. How many goats each as much as 35 cows? | |

A. 49 | B. 32 |

C. 36 | D. 41 |

**Answer : **Option A

**Explanation :**

15 cows â‰¡ 21 goats

1 cow â‰¡21/15 goats

35 cows â‰¡ (21Ã—35)/15 goatsâ‰¡(21Ã—7)/3 goatsâ‰¡7Ã—7 goats â‰¡ 49 goats

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