Question

if 1 is added to each of the two certain number their ratio is 1:2 ,if 5 id subtracted from each of the two number their ratio become 5:110,find the number​

Answer 1

Let the two numbers be x and y

According to question.

➣ ( x + 1 )/( y + 1) = 1/2

➣ 2(x + 1) = 1(y + 1)

➣ 2x + 2 = y + 1

➣ 2x - y = -2 .......(1)

And according to the second equation.

➣ (x - 4)/(y - 4) = 5/11

➣ 11(x - 4) = 5(y - 4)

➣ 11x - 44 = 5y - 20

➣ 11x - 5y = 44 - 20

➣ 11x - 5y = 24 ........( 2 )

Now multiply equation ( 1 ) with 5:-

5(2x - y = -2)

10x - 5y = -10 ....... ( 3 )

Subtracting equation (2) from equation (3):-

➣ 11x - 5y - 10x - 5y = 24 - (-10)

➣ x = 34

Now,

Substitute x in equation 1 to get the value of y:-

➣ 2x - y = -2

➣ 2(34) - y = -2

➣ -y = -68 -2

➣ y = 70

Answer 2

Correct Question :-

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

Answer :-

Let the numbers be x and y

Now according to the question -

If 1 is added to both the number and their ratio becomes 1 : 2 :-

→ $\sf \frac{x+1}{y+1} = \frac{1}{2}$

→ $\sf 2(x+1) = y + 1$

→ $\sf 2x + 2 = y + 1$

→ $\sf 2x + 2 - y - 1 = 0$

→ $\sf 2x - y + 1 = 0 \: \: \: \: \: \: \: \: \: -i$

If 5 is subtracted from each, the ratio becomes 5:11 :-

→ $\sf \frac{x - 5}{y - 5} = \frac{5}{11}$

→ $\sf 11( x - 5 ) = 5(y-5)$

→ $\sf 11x - 55 = 5y - 25$

→ $\sf 11x - 5y - 55 + 25 = 0$

→ $\sf 11x - 5y - 30 = 0\: \: \: \: \: \: \: \: \: -ii$

Multiplying equation i by 5

→ $\sf 5(2x - y + 1 = 0)$

→ $\sf = 10x - 5y + 5 = 0 \: \: \: \: \: \: \: \: \: -iii$

Equating the equation ii and iii -

→ $\sf 11x - 5y - 30 = 10x - 5y + 5$

→ $\sf 11x - 10x = 30 + 5$

→ $\sf x = 35$

Substituting in equation i

→ $\sf 2x - y + 1 = 0$

→ $\sf 2 \times 35 - y + 1 = 0$

→ $\sf 70 - y + 1 = 0$

→ $\sf 71 - y = 0$

→ $\sf y = 71$

Numbers = 35 and 71