Question

The sum of numerator and denominator of a proper fraction is 13 and their difference is 3 . Find the fraction
(a) 5/8 (b) 8/5 (c) 3/5 (d) 4/7

Answer 1

Gɪᴠᴇɴ :-

The sum of numerator and denominator of a proper fraction is 13 and their difference is 3 .

ᴛᴏ ғɪɴᴅ :-

• Fraction

sᴏʟᴜᴛɪᴏɴ :-

Let the numerator of a fraction be x and denominator be y

then,

✦ According to 1st condition :-

• Numerator + Denominator = 13

• x + y = 13. --(1)

✦ According to 2nd condition :-

• Numerator - Denominator = 3

• x - y = 3. --(2)

_______________________________

On adding (1) and (2) , we get,

↣ (x + y) + (x - y) = 13 + 3

↣ 2x = 16

↣ x = 16/2

↣ x = 8

Put x = 8 in (1) , we get,

↣ x + y = 13

↣ 8 + y = 13

↣ y = 13 - 8

↣ y = 5

Hence,

• Proper fraction is x/y = 8/5

Hence,

• Option (b) 8/5 is correct.

Answer 2

Given

The sum of numerator and denominator of a proper fraction is 13 and their difference is 3 .

Find out

Find the required fraction

Solution

★ Let the numerator be x and its denominator be y

*According to the given condition*

✧ Sum of numerator and denominator is 13

• x + y = 13 --------(i)

✧ Difference of Numerator and denominator is 3

• x - y = 3 ---(ii)

✞ Add both the equations

→(x + y) + (x - y) = 13 + 3

→ x + y + x - y = 16

→ 2x = 16

→ x = 16/2

→ x = 8

✞ Put the value of x in eqⁿ (ii)

→ x - y = 3

→ 8 - y = 3

→ y = 8 - 3

→ y = 5

Hence,

Required fraction

→ numerator/denominator = 8/5