Question

Three times the larger of two numbers gives 5 as the quotient and 5 as the remainder when divided by the smaller number. Four times the smaller number when divided by the larger number gives 2 as the quotient and 2 as the remainder. Find the numbers.

Answer 1

we will take large number x ,small number y.
then create 2 linear equations
3x/y=5+5/y  first condition,we will multiply this equation by y which will give
3x=5y+5
3x-5y=5 -our first equation(1)
 then second condition
4y/x=2+2/x multiply this by x which gives
4y=2x+2
4y-2x=2
-2x+4y=2 second equation(2)
to make x equal we multiply equation  (1) by 2 and equation (2) by 3,
 then we add (2) and (1) i.e.
2(3x-5y=5)+3(-2x+4y=2)    (WE ARE USING ELIMINATION METHOD
solving it we get                    to solve equations)
6x-6x-10y+12y=10+16
2y=16
y=16/2=8  y=8           now take equation 1 or 2 and solve for x
i will use 1
3x-5y=5
3x-5*8=5
3x=5+40 =45
x=45/3 = 15
voila

Answer 2

Please have a look at the attachment regarding the answer of this question.

Hope my answer helped !