# six bells commence tolling together and toll at intervals 2,4,6,8,10 and 12 seconds respectively. in 30 minutes how many times they toll together.

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## Six bells commence tolling together and toll at intervals of 2 4 6 8 10 12 minutes respectively In 3...

Free solutions for R S Aggarwal Solutions - Mathematics - Class 10 Chapter 2 - Real Numbers Real Numbers Exercise 1B question 27. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts

## RS Aggarwal Solutions Class 10 Mathematics Solutions for Real Numbers Exercise 1B in Chapter 1 - Real Numbers

Prev Question 27

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12

minutes respectively. In 30 hours, how many times do they toll together?

Answer:

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes

respectively.

Find LCM using prime factorization:

2 = 2 (prime number)

4 = 2 × 2 6 = 2 × 3 8 = 2 × 2 × 2 10 = 2 × 5 12 = 2 × 2 × 3

Therefore, LCM (2, 4, 6, 8, 10, 12) = 2x 2 x 2 × 3 × 5 = 120

After every 120 minutes = 2 hours, bells will toll together.

So, required number of times = (30/2 + 1) = 16 times.

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## Six bells commence tolling together and toll at intervals of 2,4,6,8,10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

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Question

## Six bells commence tolling together and toll at intervals of 2,4,6,8,10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

**A**

## 4

**B**

## 10

**C**

## 15

**D**

## 16

Easy Open in App Solution Verified by Toppr

Correct option is D)

Since, LCM of 2,4,810 and 12 is 120. So, after each 120 seconds, they would toll together,Hence, in 30 minutes, they would toll

120 30×60 =15 times

But then the question says they commence tolling together. So, they basically also toll at the beginning. So, total tolls together =15+1=16

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## [Solved] Six bells commence tolling together and toll at intervals of

Given: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. Concept used: Least common multiplication&nbs

Home Quantitative Aptitude Number System LCM and HCF LCM

## Question

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## Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

This question was previously asked in

West Bengal Police SI Previous year paper 1 (held on 15 Dec 2019)

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10 16 9 15

## Answer (Detailed Solution Below)

Option 2 : 16

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## Detailed Solution

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**Given:**

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively.

**Concept used:**

Least common multiplication

**Calculation:**

A least common multiple of (2, 4, 6, 8, 10 and 12)

we can write 2 = 1 × 2

4 = 22 6 = 2 × 3 8 = 23 10 = 2 × 5 12 = 22 × 3

A least common multiple of (2, 4, 6, 8, 10 and 12) = 23 × 3 × 5

⇒ 8 × 3 × 5 ⇒ 120 sec

Bells ring together after every 120 sec

Required number of times in 30 minutes (30 × 60 seconds ) = [(30 × 60)/120]

⇒ 15

But we have to add 1 because at starting all bells will be rung once a time after that they ring 15 times.

⇒ 15 + 1 ⇒ 16 times

**∴ The required number of times when they toll together is 16.**

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