**In a seminar, the number of participants for the subjects Hindi, English and Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them are for the same subject.**

__Question:__**Options:**

A. | 7 | |

B. | 14 | |

C. | 21 | |

D. | 28 |

**Answer: Option C**

: C

Number of rooms will be minimum if each room accomodates maximum number of participants.

In each room, the same number of participants are to be seated and all of them must be for the same subject.

∴ Number of participants in each room must be the HCF of 60, 84 and 108.

Prime factorisation of 60, 84 and 108:

60=22×3×5

84=22×3×7

108=22×33

∴ HCF =22×3=12

In each room, 12 participants can be accommodated.

Number of rooms=Total number of participants12

=60+84+10812

=25212

=21

∴ The total number of rooms is 21.

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## More Questions on This Topic :

- 5−√3
- 5+√3
- 4+√2
- 5+√9

**Answer: Option D**

: D

If p is a prime number, then √p is an irrational number.

3 is a prime number.

⇒ √3 is an irrational number.

⇒ 5−√3 is an irrational number.

Similarly,5+√3 is an irrational number.

2 is a prime number.

⇒ √2 is an irrational number.

⇒ 4+√2 is an irrational number.

9 is not a prime number.

√9=3

⇒ 5+√9=5+3=8 which is a rational number.

⇒ 5+√9 is not anirrational number.

- 10
- 11
- 12
- 27

**Answer: Option B**

: B

Euclid's division algorithm to find HCF of 1650 and 847:

Step 1: 1650 = 847 × 1 + 803

Step 2: 847 = 803 × 1 + 44

Step 3: 803 = 44 × 18 + 11

Step 4: 44 = 11 × 4 + 0 Hence, 11 is the HCF of 1650 and 847.

**Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of a measuring vessel that can be used to exactly measure the petrol from either tankers with no petrol remaining.**

__Question 5.__- 200 litres
- 170 litres
- 440 litres
- 360 litres

**Answer: Option B**

: B

Maximum capacity of the measuring vessel = HCF (850, 680)

We use Euclid's division algorithm to find the HCF of 850 and 680.

850 = 680 × 1 + 170

680 = 170 × 4 + 0

∴HCF (850, 680) = 170

So, the maximum capacity of the measuring vessel required is 170 litres.

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