Question

if 3 is subtracted from the first number and 4 is added to the second number then their ratio becomes 4:13. if 2 is subtracted from first number and 2 is added to the second then their ratio becomes 5:11find the numbers

Answer 1

First number is 7 and the second number is 9

Answer 2

Let one number be x and other be y
Then
From first statement
(x-3)/(y+4)=4/13
13x-39=4y+16
13x=4y+55
x=(4y+55)/13 -- eq 1
From second statement
(x-2)/(y+2)=5/11
11x-22=5y+10
11x=5y+32
From eq 1
11[(4y+55)/13]=5y+32
44y+605=65y+416
21y=189
y=9
Putting value of y in eq 1
x=(4×9+55)/13
x=7
Hence the numbers are 7,9