Question 19 [Assertion Reasoning] - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

Statement A (Assertion):
If product of two numbers is 5780 and their HCF is 17, then their LCM is 340 Statement

R (Reason)
:
HCF is always a factor of LCM

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

Transcript

Question 19 Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340 Statement R (Reason) : HCF is always a factor of LCM (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true.Checking Assertion
Given
Product of two numbers = 5780
HCF = 17
We know that
Product of two numbers = HCF × LCM
5780 = 17 × LCM
5780/17 = LCM
LCM = 5780/17
LCM = 340
Thus, Assertion is true
Checking Reason
HCF is always a factor of LCM
This is always true
Example:
For numbers 2 and 3
HCF = 2
LCM = 6
And, 2 is a factor of 6
Thus, HCF is always a factor of LCM
Thus, Reasoning is true
Is Reason a Correct explanation for Assertion?
Now,
Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340 Statement R (Reason) : HCF is always a factor of LCM
The formula
Product of two numbers = HCF × LCM
is not related to HCF being a factor of LCM
Therefore, Reasoning is not a correct explanation for Assertion
So,
Assertion is true
Reasoning is true
But, Reasoning is not a correct explanation for Assertion
So, the correct answer is (b)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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