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25 vote

The sum of two numbers is 216 and their HCF is 27. How many pairs of such numbers are there

Asked on by | Votes 25 | Views: 1936 | Tags: mathematics     | hcf and lcm     | quantitative aptitude     | ssc     | Add Bounty

The sum of two numbers is 216 and their HCF is 27. How many pairs of such numbers are there
1). 1
2). 2
3). 3
4). 0

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2 answers

38 vote
Answered by on | Votes 38 |
option 2 : - 2

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22 vote
Answered by on | Votes 22 | | Last Updated: 2021-07-29 14:38:16

HCF of two numbers = 27

Let the numbers be 27x and 27y where x and y are prime to each other.

According to the question, 27x + 27y = 216 27 (x + y) = 216 x + y =$\frac{216}{27}$=8

Possible pairs of x and y = (1, 7) and (3, 5)

Numbers =(27, 189) and (81, 135)

Accepted Answer