Question

The HCF of the ages of Jai and Veeru is 1 / 6 of their LCM. If the difference between the LCM and HCF of their ages is 35 and the age of Jai is 21 years; find the age of Veeru.
1. 12 years
2. 13 years
3. 14 years
4. 15 years

Answer 1

Correct Answer - Option 3 : 14 years

Given∶

HCF of the ages of Jai and Veeru = 1 / 6 of the LCM of their ages.

Difference between the LCM and HCF of their ages is Age of Jai is 21 years.

Formula Used∶

Concept of LCM and HCF

Product of two numbers = Product of their LCM and HCF

Calculation∶

HCF of their ages = 1 / 6 of LCM of their ages

⇒ LCM = 6 × HCF

Also, LCM – HCF = 35

⇒ 6 × HCF – HCF = 35

⇒ 5 × HCF = 35

⇒ HCF = 35 / 5 = 7

Now, LCM = 6 × HCF = 6 × 7 = 42

Age of Jai = 21 years;

Let the age of Veeru be ‘a’ years.

Using the formula 1^st no × 2^nd formula = HCF × LCM

So, 21 × a = 7 × 42

⇒ a = 7 × 42 / 21 = 14

∴ The age of Veeru is 14 years.