The sum of two numbers is 850 and their HCF is 25. A possible pair of such numbers is :

Correct option is A

Given:

Sum of two numbers = 850

HCF of the numbers = 25

Solution:
If the HCF of two numbers is hh, then the numbers can be written as 25a and 25b where gcd(a, b) = 1. Their sum:

a + 25b = 25(a + b) = 850

a + b =$$\frac{850}{25}$$​ = 34

Now, co-prime pairs (a, b) such that a + b = 34

Possible co-prime pairs with sum 34:

(3, 31) → valid

(5, 29) → valid

(15, 19) → valid

(9, 25)→ valid

Choosing one valid pair: (9, 25)
Then the numbers = 25 × 9 = 225 and 25 × 25 = 625