Question

the ratio of two number is 2/3 if two a subtracted from the first and 8 from second ratio .the ratio become the reciprocal of the original ratio. find the number.​

Answer 1

Answer:

• The 1st number and 2nd number are 8 and 12 respectively.

Step-by-step explanation:

Given that:

• The ratio of two numbers is 2 : 3.
• If 2 is subtracted from the first number and 8 is subtracted from the second number, the ratio becomes reciprocal of the original ratio.

To Find:

• The numbers.

Let us assume:

• The numbers be 2x and 3x respectively.

After subtracting 2 and 8 from the numbers,

• 1st number = 2x - 2
• 2nd number = 3x - 8

According tot he question:

$\sf{\longmapsto(2x-2):(3x-8)=Reciprocal\;of\;2:3}$

$\sf{\longmapsto(2x-2):(3x-8)=3:2}$

Writing as fraction,

$\sf{\longmapsto\dfrac{2x-2}{3x-8}=\dfrac{3}{2}}$

By cross-multiplication,

$\sf{\longmapsto2(2x-2)=3(3x-8)}$

Opening the brackets,

$\sf{\longmapsto4x-4=9x-24}$

Transposing variables to LHS, constants to RHS and changing its sign,

$\sf{\longmapsto4x-9x=-24+4}$

Solving further,

$\sf{\longmapsto-5x=-20}$

$\sf{\longmapsto5x=20}$

Transposing 5 from LHS and changing its sign,

$\sf{\longmapsto x=\dfrac{20}{5}}$

Dividing RHS,

$\sf{\longmapsto x=4}$

Hence,

• x = 4

Therefore,

• 1st number = 2x = 2 × 4 = 8
• 2nd number = 3x = 3 × 4 = 12