The HCF and the LCM of two numbers are 35 and 840 respectively If the ratio of the two numbers is 3 ...........

Quantitative Aptitude (MTS) LCM, HCF

The HCF and the LCM of two numbers are 35 and 840, respectively. If the ratio of the two numbers is 3 : 8, then the smaller of

the two numbers is:

This questions was previously asked in

SSC MTS 20th July 2022 Shift-3

280

105

210

To solve this, let's use the properties of HCF and LCM along with the given ratio.

- The HCF (Highest Common Factor) of two numbers is given as 35, and the LCM (Lowest Common Multiple) is 840.

- The ratio of the two numbers is provided as 3:8.

- We can assume the two numbers to be 3x and 8x.

- According to the relationship between two numbers, their HCF, and LCM:

`(Number1 * Number2) = HCF * LCM`

- Substitute the values:

`(3x * 8x) = 35 * 840`

- Simplify:

`24x^2 = 29400`

- Solving for x gives:

`x^2 = 1225`

`x = 35`

- The smaller number = 3x = `3 * 35 = 105`

?? Correct Answer: Option 3 - 105

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