Question

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4
when 8 is added to its denominator. Find the fraction.​

Answer 1

Given

• When one is subtracted from the numerator a fraction it becomes ⅓
• The same fraction becomes ¼ when eight is subtracted from the denominator

To Find

• The Fraction

Solution

☯ Assume the fraction to be x/y

★ According to the given Question :

→ (x-1)/y = ⅓

→ 3(x-1) = 1 × y

→ 3x-1 = y ❲ eq(1) ❳

Similarly,

→ x/(y+8) = ¼

→ x × 4 = 1(y+8)

→ 4x = y+8

→ 4x-y = 8 ❲ eq(2) ❳

━━━━━━━━━━━━━━

• Subtracting eq(2) from eq(1) we'll get the value of x which we may substitute in eq(1) to get the value of y

→ (3x-1) - (4x-y) = y-8

→ 3x - 4x + y = -8 + 1

→ -x = -7

→ x = 7

Substituting this on eq(1)

→ 3×7 - 1 = y

→ 21 - 1 = y

→ y = 20

Therefore,

• x/y = 7/20

∴ The fraction in this case is 7/20

Answer 2

Heya !

Question:-

• A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Given:-

• When 1 is subtracted from numerator it becomes 1/3.
• when 8 is added to the denominator it becomes 1/4.

To find:-

• original fraction.

Solution:-

Let the numerator be X and denominator be Y.

according to the question:-

$\implies$(x-1)/y = 1/3

$\implies$3( x-1 )= y

$\implies$ 3x-3 = y

$\implies$ 3x - y = 3 ............. eq. 1

second condition:-

$\implies$ X/y+8 = 1/4

$\implies$ 4x = y+8

$\implies$ 4x - y = 8 .............. eq. 2

Subtracting eq. 2 from eq.1

$\implies$ 4x - y = 8

$\implies$ 3x - y = 3

- + -

X = 5

Hence, we got the value of X as 5

and Y = 8 - 4(5) ......... from eq. 2

$\implies$ y = 8-20

$\implies$ y = -12

Hence, the fraction becomes 5/-12

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Hope it helps ⭐⭐⭐