# Problems on Chain Rule

Q1. Running at the same constant rate, 5 identical machines can produce 2500 bottles per minute. At this rate, how many bottles could 10 such machines produce in 5 minutes ?

(a) 2500

(b) 25000

(c) 7500

(d) 75000

**Answer:** (b) 25000

In 1 minute 5 machine can produce = 2500 bottles

∴ In 5 minute 5 machine can produce = 5 X 2500 bottles

∴ In 5 minute 1 machine can produce = (5 X 2500)/5 bottles

∴ In 5 minute 10 machine can produce = (5 X 2500 X 10)/5 bottles = 25000 bottles

Q2. In a hospital, there is a consumption of 1250 liters of milk for 50 patients for 30 days. How many patients will consume 1750 liters of milk in 25 days

(a) 62 patients

(b) 73 patients

(c) 84 patients

(d) 92 patients

**Answer:** (c) 84 patients

In 30 days 1250 liters of milk consume by 50 patient

∴ In 25 days 1250 liters of milk consume by (50X30)/28 patient

∴ In 25 days 1750 liters of milk consume by (50X30X1750)/(25X1250) patient = 84 patient

Q3. A contractor under takes to build a wall in 50 days. He employes 50 people for the same. However after 25 days, he finds that only 40% of the work is complete. How many more men need to be employeed to complete the work in time ?

(a) 22

(b) 25

(c) 29

(d) 33

**Answer:** (b) 25

Work done = 40% = 40/100 = 2/5

Remaining work = (1 - ^{2}/_{5}) = 3/5

2/5 work is done in 25 days by 50 peoples

∴ 1 work is done in 25 days by (50X5)/2 peoples

∴ 3/5 work is done in 25 days by (50X5X3)/(2X5) peoples = 75 people

∴ Required no. of people = 75 - 50 = 25

Q4. A garrison of 600 men had provisions for 30 days. After 3 days, a reinforcement of 200 men arrived. The remaining food will now last for how many days.

(a) 20¼ days

(b) 22¾ days

(c) 25½ days

(d) 27¾ days

**Answer:** (a) 20¼ days

After 3 days

600 men had provisions for 27 days

∴ 1 men had provision for = 27 X 600 days

∴ (600 + 200) men had provisions for = | 27 X 600 | days = | 27 X 600 | days = | 81 | days = 20¼ days |

(600 + 200) | 800 | 4 |

Q5. Two persons can complete a piece of work in 9 days. How many more persons are neede to complete the double work in 12 days ?

(a) 1

(b) 2

(c) 4

(d) 5

**Answer:** (a) 1

Two persons can complete a work in 9 days

∴ Two persons can complete double work in 9 X 2 days = 18 days

In 18 days double work can complete by 2 persons

∴ In 1 days double work can complete by 2 X 18 persons

∴ In 12 days double work can complete by (2X18)/12 persons = 3 persons

∴ Required persons = 3 - 2 = 1

Q6. If 6 spiders can catch 12 flies in 6 minutes, how many flies can 60 spiders can catch in 60 minutes ?

(a) 800

(b) 900

(c) 1050

(d) 1200

**Answer:** (d) 1200

In 6 minute 6 spiders can catch = 12 flies

∴ In 1 minute 6 spiders can catch = 12/6 flies

∴ In 60 minute 6 spiders can catch = (12X60)/6 flies

∴ In 60 minute 1 spiders can catch = (12X60)/(6X6) flies

∴ In 60 minute 60 spiders can catch = (12X60X60)/(6X6) flies = 1200 flies

Q7. If the rent for grazing 36 cows for 18 days is Rs. 600, how many cows can graze for 20 days on Rs. 500 ?

(a) 24 days

(b) 27 days

(c) 29 days

(d) 32 days

**Answer:** (b) 27 days

In 18 days rent be Rs. 600 for grazing = 36 cows

∴ In 1 days rent be Rs. 600 for grazing = 36X18 cows

∴ In 20 days rent be Rs. 600 for grazing = | 36 X 18 |

20 |

∴ In 20 days rent be Rs. 1 for grazing = | 36 X 18 |

20 X 600 |

∴ In 20 days rent be Rs. 500 for grazing = | 36 X 18 X 500 | = 27 days |

20 X 600 |

Q8. 25 men can reap a field in 20 days. When should 15 men leave the work if the whole field is to be reaped in 37½ days after they leave the work ?

(a) 5 days

(b) 8 days

(c) 11 days

(d) 14 days

**Answer:** (a) 5 days

Let 15 men work for x days

Work done = x/20, Remaining work = (1 - x/20)

25 men's 1 day's work = ^{1}/_{20}

1 men 1 day's work = 1/(20 X 25) = ^{1}/_{500}

10 men's 1 day's work = ( | 1 | X 10 ) = | 1 |

500 | 50 |

10 men's 75/2 day's work = ( | 1 | X | 75 | ) = | 3 |

50 | 2 | 4 |

∴ ( 1 - | x | ) = | 3 |

20 | 4 |

⇒ | 20 - x | = | 3 |

20 | 4 |

⇒ 80 - 4x = 60

⇒ 4x = 20

⇒ x = 5 days

Q9. 9 men complete one-third of a piece of work in 10 days. How many more men should be employeed to finish the rest of the work in 15 more days ?

(a) 2

(b) 3

(c) 5

(d) 6

**Answer:** (b) 3

Work done = ^{1}/_{3}

Remaining work = (1 - ^{1}/_{3}) = ^{2}/_{3}

In 10 days ^{1}/_{3} of a work can done by 9 men

∴ In 10 days 1 of a work can done by 9 X 3 men

In 10 days ^{2}/_{3} of a work can done by |
9 X 3 X 2 | men |

3 |

In 15 days ^{2}/_{3} of a work can done by |
9 X 3 X 2 X 10 | = 12 men |

3 X 15 |

∴ Required no. of men = 12 - 9 = 3

Q10. If 4 persons weave 300 shawls in 12 days, how many shawls will 8 persons weave in 7 days ?

(a) 295

(b) 305

(c) 325

(d) 350

**Answer:** (d) 350

In 12 days 4 persons weave = 300 shawls

∴ In 1 days 4 persons weave = | 300 | shawls |

12 |

∴ In 7 days 4 persons weave = | 300 X 7 | shawls |

12 |

∴ In 7 days 1 persons weave = | 300 X 7 | shawls |

12 X 4 |

∴ In 7 days 8 persons weave = | 300 X 7 X 8 | shawls = 350 |

12 X 4 |

**1**