Question

If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3 . Find the fraction.
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Answer 1

❥ Qᴜᴇsᴛɪᴏɴ :-

If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3 . Find the fraction.

❥ Gɪᴠᴇɴ :-

If we add 2 to the numerator of fraction it reduces 1/2

If 1 is subtracted from the denominator it reduces 1/3

❥ Tᴏ Fɪɴᴅ :-

Fraction

❥ Sᴏʟᴜᴛɪᴏɴ :-

Let the fraction be x

According to 1st condition, if we add 2 to the numerator it reduces 1/2

⟾ x + 2/y = 1/2

⟾ (x + 2)2 = y

⟾ y = 2x + 4 __________①

According to 2nd condition

If we subtract 1 from the fraction it reduces 1/3

⟾ x/y - 1 = 1/3

⟾ 3x = y - 1

⟾ x = y-1/3__________②

Now, substituting value of y from ①st equation in ②nd equation

⟾ x = (2x + 4)-1 / 3

⟾ 3x = 2x + 3

⟾ 3x - 2x = 3

⟾ x = 3

Putting value of x in ①st equation

⟾ y = 2 × 3 + 4

⟾ y = 6 + 4

⟾ y = 10

⛬ Fraction = 3/10

Answer 2

❍ Given ❍

If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3

❍ To find ❍

Find the required fraction

❍ Solution ❍

✞ Let the required fraction be x/y

➣ If 2 is added to the numerator of the fraction, it reduces to 1/2

• x + 2/y = 1/2 --- (i)

➣ 1 is subtracted from the denominator, it reduces to 1/3

• x/y - 1 = 1/3 ---- (ii)

✞ From (i)

➨ x + 2/y = 1/2

➨ y = 2(x + 2)

➨ y = 2x + 4

➣ By substitution method

Substitute the value of y in eqⁿ (ii)

➨ x/y - 1 = 1/3

➨ x/2x + 4 - 1 = 1/3

➨ x/2x + 3 = 1/3

➨ 3x = 2x + 3

➨ 3x - 2x = 3

➨ x = 3

➣ Putting the value of x in y = 2x + 4

➨ y = 2x + 4

➨ y = 2 × 3 + 4

➨ y = 6 + 4

➨ y = 10

**Hence, the required fraction = x/y

= 3/10