Solution of question from book:
Secondary school Mathematics for Class 10 R S Aggarwal V Aggarwal
Unit 1: Number system
Chapter 1.1: Real numbers
Exercise 1B
Question:
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?
Solution:
The time gap between the tolling of each bells are 2,4,6,8,10,12 minutes respectively.
It means that when all the bells toll together first simultaneously, after that each bells toll at different time intervals which are of 2,4,6,8,10,12 minutes respectively.
For this we will find the L.C.M of the given time intervals of each bells.
LCM of 2,4,6,8,10,12
LCM = 2 x 2 x 2 x 3 x 5 = 120 minutes
This 120 minutes means that all the bells tolls together after every 120 minutes or 2 hours.
Now the question is asking that in 30 hours how many times do they toll together.
Therefore dividing 30 by 2 and adding 1 to it, we get the number of times of their tolling simultaneously.
Therefore all the bells toll together 16 times in 30 hours.
Tip:
Here in this question the number of hours is 30 which is an even number.
Now if this number of hours is given an odd number, then what we will do because 31 is not exactly divisible by 2(Here 2 is taken as reference from the above question).
To solve such type of questions we will first add 1 to the given number of hours, and then divide the sum we get as result.
Question if hours given is an odd number:
Six bells commence tolling together and toll at intervals of 2,4,6,8,10,12 minutes respectively. In 31 hours, how many times do they toll together?
Solution:
The time gap between the tolling of each bells are 2,4,6,8,10,12 minutes respectively.
It means that when all the bells toll together first simultaneously, after that each bells toll at different time intervals which are of 2,4,6,8,10,12 minutes respectively.
For this we will find the L.C.M of the given time intervals of each bells.
LCM of 2,4,6,8,10,12
LCM = 2 x 2 x 2 x 3 x 5 = 120 minutes
This 120 minutes means that all the bells tolls together after every 120 minutes or 2 hours.
Now the question is asking that in 31 hours how many times do they toll together.
Therefore first adding 1 to the given number of hours and then dividing by 2, we get the number of times of their tolling simultaneously.
Therefore all the bells toll together 16 times in 31 hours.
Watch the video solution of the above question by clicking this link:
Question : 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?
Video solution:
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