The product of 2 two-digit numbers is 300 and their HCF is 5. What are

1.	The product of 2 two-digit numbers is 300 and their HCF is 5. What are the numbers?
Answer» Given that HCF of 2 numbers is 5 The numbers may like 5x and 5y Also given their product = 300 5x × 5y = 300 ⇒ 25xy = 300 ⇒ xy = 300/25 ⇒ xy = 12 The possible values of x and y be (1, 12) (2, 6) (3, 4) The numbers will be (5x, 5y) ⇒ (5 × 1, 5 × 12) = (5, 60) ⇒ (5 × 2, 5 × 6) = (10, 30) ⇒ (5 × 3, 5 × 4) = (15, 20) (5, 60) is impossible because the given the numbers are two digit numbers. The remaining numbers are (10, 30) and (15, 20) But given that HCF is 5 (10, 30) is impossible, because its HCF = 10 The numbers are 15, 20

The product of 2 two-digit numbers is 300 and their HCF is 5. What are the numbers?

Answer»

Given that HCF of 2 numbers is 5

The numbers may like 5x and 5y

Also given their product = 300

5x × 5y = 300

⇒ 25xy = 300

⇒ xy = 300/25

⇒ xy = 12

The possible values of x and y be (1, 12) (2, 6) (3, 4)

The numbers will be (5x, 5y)

⇒ (5 × 1, 5 × 12) = (5, 60)

⇒ (5 × 2, 5 × 6) = (10, 30)

⇒ (5 × 3, 5 × 4) = (15, 20)

(5, 60) is impossible because the given the numbers are two digit numbers.

The remaining numbers are (10, 30) and (15, 20)
But given that HCF is 5

(10, 30) is impossible, because its HCF = 10

The numbers are 15, 20