Question

The denominator of a fraction is 1 less than 4 times the numerator. Denominator

becomes 12 times the numerator, if both the numerator and the denominator are

reduced by 3. Find the fraction.​

Answer 1

Let the numerator be x and then the denominator should be 4x - 1 (1 less than 4 times x).

If both are reduced by 3, numerator is (x) - 3 = x - 3 whereas denominator is (4x - 1) - 3 = 4x - 4.

According to the question denominator is 12 times of numerator, now.

=> denominator = 12 × numerator

=> 4x - 4 = 12(x - 3)

=> 4x - 4 = 12x - 36

=> 36 - 4 = 12x - 4x

=> 32 = 8x

=> 4 = x

Therefore the required fraction is x/(4x - 1) = 4/(4*4 - 1) = 4/(16 - 1) = 4/15

Fraction is 4/15.

Answer 2

GivEn:

• The denominator of a fraction is 1 less than 4 times the numerator.
• Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 3.

To find:

• The fraction.

Solution:

• Let the fraction be N/D & N be x.

Given that, The denominator of a fraction is 1 less than 4 times the numerator.

• In numerical form this implies,

• x/4x - 1

Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 3.

• x - 3/(4x - 1) - 3

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Let's form a equation using the given values,

→ 4x - 1 - 3 = 12(x - 3)

→ 4x - 4 = 12x - 36

→ 4x - 12x = -36 + 4

→ -8x = -32

→ x = -32/-8

→ x = 4

∴ Hence, The required fraction is x/4x - 1 = 4/4(4) - 1 i.e 4/15