Question

If three times the larger of two numbers is divided by the smaller we get 4 as quotient and 8 as reminder. If five times the smaller is divi
ded by the larger we get 3 as quotientand 5 as remainder. Find the numbers

Answer 1

Note:  We know that Dividend = Divisor * Quotient + Remainder. 

Let the larger number be x and the smaller number be y.

Given that 3 times, the larger number is divided by smaller we get 4 as Quotient and 8 as remainder.

= > 3x = y * 4 + 8

= > 3x = 4y + 8

= > 3x - 4y = 8   --------- (1)


Given that if five times the smaller is divided by larger we get 3 as Quotient and 5 as remainder.

= > 5y = 3x + 5

= > 5y - 3x = 5   

= > -3x + 5y = 5  --------- (2)


On solving (1) & (2), we get

= >  3x - 4y = 8

= > -3x + 5y = 5

     --------------------

              y = 13


Substitute y = 13 in (1), we get

= > 3x - 4y = 8

= > 3x - 4(13) = 8

= > 3x - 52 = 8

= > 3x = 52 + 8

= > 3x = 60

= > x = 60/3

= > x = 20.

Therefore the numbers are 20, 13.


Verification:

= > 3 * x = 4 * y + 8

= > 3(20) = 4 * 13 + 8

= > 60 = 52 + 8

= > 60 = 60.




Hope this helps!

Answer 2

Answer:

Hope it will help you

Step-by-step explanation:

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