Question

The ratio of two numbers is 2/3.
If 2 is subtracted from the first and 8 from the second,
the ratio becomes the reciprocal of the original ratio. Find the numbers.​

Answer 1

Answer:

8 and 12

Step-by-step explanation:

Let the ratio be

y

x

=

3

2

⇒3x=2y

⇒3x−2y=0 --- (1)

Given, if 2 is subtracted from x and 8 from y, then ratio =

y−8

x−2

=

2

3

⇒2x−4=3y−24

⇒2x−3y=−20 --- (2)

Multiplying (1) with (2), we get,

6x−4y=0 ----(3)

Multiplying (2) with (3), we get,

6x−9y=−60 -----(4)

Subtracting (4) from (3), we get

y=12

Substituting y=12 in the (1), we get

x=8

Hence, the numbers are 8 and 12

Answer 2

Answer:

8 and 12

Step by Step explanation:

Let’s assume the two numbers to be x and y.

Given that the ratio of the numbers = 2/3

Then,

x/y = 2/3

3x = 2y

⇒ 3x – 2y = 0 … (i)

Also given, if 2 is subtracted from the first and 8 from the second, the ratio becomes the reciprocal of the original ratio

(x – 2)/(y – 8) = 3/2

2 (x – 2) = 3 (y – 8)

2x – 4 = 3y – 24

⇒ 2x – 3y = -20 … (ii)

Now, performing 3 x (i) – 2 x (ii) we get

9x – 6y = 0

4x – 6y = -40

(-)–(+)—-(+)—

5x = 40

x = 40/5

x = 8

On substituting the value of x in (i), we get

3(8) – 2y = 0

24 = 2y

y = 24/2 = 12

Therefore, the numbers are 8 and 12.