Question

if 1 is added to each of the two numbers,their ratio becomes 1:2 and when 5 is subtracted from each of these, the ratio becomes 5:11. Find the numbers


and the answer is x=35,y=71 Please explain ​

Answer 1

Answer: x=35 and y=71

Step-by-step explanation:

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

SOLUTION :-

Let,

First number = x

Second number = y

According to the first condition,

$\longrightarrow\sf \dfrac{x+1}{y+1}= \dfrac{1}{2} \\\\\longrightarrow 2(x+1)= y+1 \\\\\longrightarrow 2x+2= y+1 \\\\\longrightarrow 2x-y= -1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x-5}{y-5}=\dfrac{5}{11} \\\\\longrightarrow 11(x-5)= 5(y-5) \\\\\longrightarrow 11x-55= 5y-25 \\\\\longrightarrow 11x-5y = 30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............(2)$

Multiply equation (1) by 5,

$\longrightarrow\sf 10x-5y=-5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............(3)$

Equation (2) - Equation (3),

$\longrightarrow\bf x = 35$

Substitute the value of x in equation (1),

$\longrightarrow\sf 2\times 35- y = -1 \\\\\longrightarrow 70-y = -1 \\\\\longrightarrow -y = -71\\\\\longrightarrow\bf y = 71$

First number = 35

Second number = 71