Question

The sum of two numbers is 232. Their hcf is 29. Which of these pairs give the possible values of the numbers?

Answer 1

The sum of two numbers is 232 and their HCF is 29.

To find : The numbers are ...

solution : here HCF of 29. so the numbers are ; 29a , 29b [ where a and b are co - prime numbers ]

given sum of two numbers = 232

⇒29a + 29b = 232

⇒a + b = 8

we can assume that a = 5 , b = 3 or a = 1, 7

so the numbers are ; 29a = 29 × 5 = 145

29b = 29 × 3 = 87

another pair of numbers is ; 29a = 29 × 1 = 29

29b = 29 × 7 = 203

Therefore the pairs of the numbers are (145, 87) and (29, 203).