Question

Maths Question of linear equation in two variables :

Q: If x and y are the two digit of the number 653xy such that, these number is divisible by 80. Find the value of x and y.

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Answer 1

80 = 5×2×8

653xy is divisible by 2 and 5 both, so y = 0
653x should be divisible by 8
It will be happen than x = 6
so x = 6 and y = 0

Answer 2

Answer :

x + y = 6 ( Option D )

Explanation :

Given that ,

653xy is divisible by 80.

In this case , we know the factors of 80 :-

80 = 5 × 16 ( Co - primes )

To be divisible by 5, the unit digit(y) should either be 0 or 5.

Means , y = 0 or 5.

Now , we include another factors of 80 :-

80 = 8 × 10

Here , the unit digit(y) should also be divisible by 10.

So , y = 0 or 5 ( where 5 by gets excluded )

Now ,

=> y = 0

So , now we have the number :- 653x0

Again , the divisibility of 16 says that all the last four digits should be divisible by 16 :-

=> 53x0/16

Assuming the value of x = 6.

After the division , ( refer to the attachment )

We obtain the results as :-

Quotient = 335

Remainder = 0

And X = 6.

Now ,

=> x = 6.

So , we have the values of both x and y i.e. 6 and 0 respectively.

Then ,

=> x + y = 6 + 0 = 6 ( Answer )