Question

If we added 5 to the denominator and subtract 5 from the numerator of a fraction. it reduce to 1/8. If we subtract 3 from the numerator and add 3 to its denominator, it reduces to 2/7. Find the fraction

Answer 1

Gɪᴠᴇɴ :-

If we added 5 to the denominator and subtract 5 from the numerator of a fraction. it reduce to 1/8. If we subtract 3 from the numerator and add 3 to its denominator, it reduces to 2/7.

ᴛᴏ ғɪɴᴅ :-

Fraction

sᴏʟᴜᴛɪᴏɴ :-

Let the fraction be x/y

Then,

• ✟ According to 1st condition :-

$\implies \frac{(x - 5)}{(y + 5)} = \frac{1}{8} \\ \\ \implies \: 8(x - 5) = 1(y + 5) \\ \\ \implies \: 8x - 40 = y + 5 \\ \\ \implies \: 8x - 40 - 5 = y \\ \\ \implies \: (8x - 45) = y$

We get,

➦ y = (8x - 45) -----(1)

Now,

• ✟ According to 2nd Condition :-

$\implies \: \frac{</u></strong><strong><u>(</u></strong><strong><u>x - 3</u></strong><strong><u>)</u></strong><strong><u>}{</u></strong><strong><u>(</u></strong><strong><u>y + 3)} = \frac{2}{7} \\ \\ \implies \: 7(x - 3) = 2(y + 3) \\ \\ \implies \: 7x - 21 = 2y + 6 \\ \\ \implies \: 7x - 2y = 6 + 21 \\ \\ \implies \: 7x - 2y = 27$

We get,

➦ 7x - 2y = 27. ----(2)

✑ On putting the value of (1) in (2) , we get,

↣ 7x - 2(8x - 45) = 27

↣ 7x - 16x + 90 = 27

↣ -9x = 27 - 90

↣ -9x = -63

↣ x = -63/-9

↣ x = 7

Now,

✑ Put the value of x in (1) , we get,

↣ y = (8x - 45)

↣ y = (8×7 - 45)

↣ y = 56 - 45

↣ y = 11

Hence,

➲ Fraction is x/y = 7/11