Question

If 1 is added to each of the given two numbers, then their ratio is 1:2. If 5 is subtracted from each of the numbers, then their ratio is 5:11. Find the numbers.​

Answer 1

Let the no.s be x and y.

given, A/Q,

x+1:y+1 = 1:2

x+1÷y+1 = 1÷2

2x+2 = y+1

2x-y = -1        (1)

Again, x-5:y-5 = 5:11

x-5÷y-5 =  5÷11

11x-55 = 5y-25

11x-5y = 30     (2)

from 1 and 2, by elimination method,

(1)x5⇒ 10x-5y = -5

(2)x1⇒ 11x-5y = 30

___  (-)   (+)     (-)_

        -1x        = -35, so, x = 35

We know, from (1)

2x-y = -1

putting x==35, we get

2×35+1 = y

71 = y

so the no.s are 30 and 71.

Answer 2

Let the no. be x & y.

x+1/y+1 =1/2

2x-1=y —(1)

x-5/y-5= 5/11

11x-5y= 30 —(2)

Put 1 in 2

11x-5(2x+1) = 30

x= 35 y= 71.