Question

Two numbers are in the ratio of 6: 8. If 10 is subtracted from each, the new numbers are in
the ratio 16:32. Find the smaller number.
i) 22
ii) 12
iii) 38
iv) 15
PLS GIVE THE ANSWER WITH EXPLANATION TOO

Thank you ​

Answer 1

Let the two numbers be x and y.

As per condition 1, i.e., Two numbers are in the ratio 5:6.

The equation becomes,

y

x

=

6

5

∴6x−5y=0 ..........(1)

As per condition 2, If 8 is subtracted from each of the numbers the ratio is 4:5.

The equation becomes,

y−8

x−8

=

5

4

∴5x−4y=8 ...........(2)

Equation (1) can be written as x=

6

5y

Substituting x=

6

5y

in (2) we get,

y=48

Re substituting y=48 in (1) we get,

x=40

Hence Numbers are 40,48.