Question

the numerator of a number is 5 less than its denominator . if the denominator is increased by 7 and numerator by 3 we get the fraction is 3/5 what is the fraction

Answer 1

Given:

✰ The numerator of a number is 5 less than its denominator.

✰ If the denominator is increased by 7 and numerator by 3 we get the fraction is 3/5.

To find:

✠ The fraction.

Solution:

We will assume and consider the denominator as x and we know, the numerator of a number is 5 less than its denominator, which means that 5 will be substracted from the denominator.

Let the denominator be x.

then, the numerator = x - 5

➛ Fraction = (x - 5)/x

Now, if the denominator is increased by 7 i.e, we will add 7 to the denominator and numerator increased by 3 i.e, we will add 3 to the numerator, we get the fraction is 3/5.

According to question,

➤ (x - 5 + 3 )/(x + 7) = 3/5

➤ (x - 2 )/(x + 7) = 3/5

By cross-multiplication method,

➤ 5( x - 2 ) = 3(x + 7)

➤ 5x - 10 = 3x + 21

➤ 5x - 3x = 21 + 10

➤ 2x = 31

➤ x = 15.5

➛ Original fraction = (x - 5)/x

➛ Original fraction = ( 15.5 - 5)/15.5

➛ Original fraction = 10.5/15.5

∴ The Fraction = 10.5/15.5

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