Question

The sum of two numbers is 1215 and their hcf is 81

Answer 1

Answer:

Let the number be 81a and 81b where a and b are two numbers prime to each other.

∴ 81a + 81b = 1215

⇒ a + b = 1215/81 = 15

Now, find two numbers, whose sum is 15, the possible pairs are (14, 1) , (13, 2), (12, 3), (11, 4), (10, 5), (9, 6 ), (8, 7) of these the only pairs of numbers that are prime to each other are (14, 1) , (13, 2), (11, 4), and (8, 7).

Hence, the required number are  

(14 x 81, 1 x 81), (13 x 81, 2 x 81), (11 x 81, 4 x 81), (8 x 81, 7 x 81)

or (1134, 81), (1053, 162), (891, 324), (648, 567)

So, there are four such pairs .

Answer 2

Answer:

Nos are 81 and (1215-8l)

81 and 1134. Ans