Question

one number is greater than thrice the other number by 2.if 4 times the smaller number exceeds the greater by 5,find the number

Answer 1

let 1st no. be x and 2nd be y
as x is greater than 3x by 2
so x-3y=2.....................(i)
as from eq (i) we can observe that y is smaller than x
so, 4y-x=5;...............(ii)
adding eq (i) and (ii)
  x-3y=2
 -x+4y=5
⇒4y-3y=7
⇒y=7
substituting value of y in eq(i)
we get x-21=2
⇒x=23

the nos. are 7 and 23    (ans)

Answer 2

Let the greater number be x and the smaller number be y.
x - 2 = 3y
4y - 5 = x
Adding both equations we get:
x - 2 + 4y - 5 = 3y + x
x - 7 + 4y = 3y + x
x - x - 7 = 3y - 4y
- 7 = - y (both minus gets cancelled)
y = 7
x = 7 * 3 + 2
x = 23
Greater number is 23 and the smaller number is 7.