Question

if two numbers are in the ratio 2:3 and the product of their Hcf and Lcm is 12150 then the sum of the number is​

Answer 1

Step-by-step explanation:

ANSWER

Let the numbers be 2x and 3x Then

2x×3x=33750⇒6x2=33750

⇒x2=5625⇒x2=54×32

⇒x=52×3=75

∴ The two numbers are 2 x 75 and 3 x 75 i.e.

150 and 225

∴ Required sum =150+225=375

Answer 2

Given :-

If two numbers are in the ratio 2:3 and the product of their Hcf and Lcm is 12150

To find :-

Sum of number

Solution :-

• Numbers are in ratio = 2 : 3
• Product of LCM and HCF = 12150

As we know that

Let the number be y

• First number = 2y
• Second number = 3y

According to question

→ HCF × LCM = Product of two numbers (First number × second)

→ HCF × LCM = a × b

→ 12150 = 2y × 3y

→ 12150 = 6y²

→ y² = 12150/6

→ y² = 2025

→ y = √2025

→ y = 45

Hence,

• First number = 2y = 2*45 = 90
• Second number = 3y = 3*45 = 135

Now, sum of two numbers

• First number + second number
• 90 + 135 = 225

Verification :-

• HCF × LCM = Product of two numbers

• LHS = HCF × LCM
• RHS = Product of two numbers

→ RHS = Product of two numbers

→ First number × second number

→ 90 × 135

→ 12150 = LHS

• LHS = RHS = 12150 Verified