Question

4. The numerator of a fraction is 1 less than the denominator. If numerator is decreased by 2 and denominator is increased by 3, the fraction becomes / . Find the fraction.

Answer 1

Correct Question

The numerator of a fraction is 1 less than the denominator. If numerator is decreased by 2 and denominator is increased by 3, the fraction becomes 1/4 .Find the fraction

Solution

★Let the denominator be x and numerator be (x - 1)

According to the given condition

Numerator of a fraction is 1 less than the denominator. If numerator is decreased by 2 and denominator is increased by 3, the fraction becomes 1/4 .

→ x - 1 - 2/x + 3 = 1/4

→ x - 3/x + 3 = 1/4

→ x + 3 = 4(x - 3)

→ x + 3 = 4x - 12

→ x - 4x = -12 - 3

→ -3x = -15

→ x = 15/3 = 5

Hence,

Required fraction = x - 1/x = 5 - 1/5 = 4/5

Answer 2

CORRECT QUESTION :-

The numerator of a fraction is 1 less than the denominator. If numerator is  decreased by 2 and denominator is increased by 3, the fraction becomes 1/4. Find the  fraction.

GIVEN

• The numerator of a fraction is 1 less than the denominator.

• If numerator is decreased by 2 and denominator is increased by 3, the fraction becomes 1/4 .

TO FIND

The fraction.

SOLUTION

Let the denominator be x. Then the numerator becomes (x - 1).

A/q,

$\displaystyle{\sf{\frac{x-1-2}{x+3}=\frac{1}{4} }}\\\\\displaystyle{\sf{\longrightarrow \frac{x-3}{x+3}=\frac{1}{4} }}\\\\\displaystyle{\sf{\longrightarrow x+3=4(x-3) }}\\\\\displaystyle{\sf{\longrightarrow x+3=4x-12 }}\\\\\displaystyle{\sf{\longrightarrow 3+12=4x-x }}\\\\\displaystyle{\sf{\longrightarrow 15=3x }}\\\\\displaystyle{\sf{\longrightarrow x=\frac{15}{3} }}\\\\\boxed{\displaystyle{\sf{\longrightarrow x=5}}}$

The required fraction is :-

$\displaystyle{\sf{\frac{x-1}{x} }}\\\\\displaystyle{\sf{=\frac{5-1}{5} }}\\\\\underline{\boxed{\boxed{\displaystyle{\sf{=\frac{4}{5} }}}}}$

Therefore, the required fraction is 4/5.