Question

2)A fraction becoms 1/2 if I is added to the numerator and Denominator and it becomes 1/3 when 1 is subracted from the numerator and 2 is added to Denominator


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Answer 1

GIVEN

fraction becoms 1/2 if I is added to the numerator and Denominator and it becomes 1/3 when 1 is subracted from the numerator and 2 is added to Denominator

TO FIND

Find the required fraction

SOLUTION

Let the required fraction be x/y

**According to the given condition**

★ A fraction becoms 1/2 if 1 is added to the numerator and denominator

→ x + 1/y + 1 = 1/2

→ 2(x + 1) = 1(y + 1)

→ 2x + 2 = y + 1

→ 2x - y = 1 - 2

→ 2x - y = - 1 ---(i)

★ It becomes 1/3 when 1 is subracted from the numerator and 2 is added to Denominator

→ x - 1/y + 2 = 1/3

→ 3(x - 1) = 1(y + 2)

→ 3x - 3 = y + 2

→ 3x - y = 3 + 2

→ 3x - y = 5 ---(ii)

Subtract both the equations

→ (2x - y) - (3x - y) = - 1 - 5

→ 2x - y - 3x + y = -6

→ - x = - 6

→ x = 6

Putting the value of x in equation (i)

→ 2x - y = - 1

→ 2×6 - y = -1

→ 12 - y = -1

→ y = 12 + 1

→ y = 13

Hence,

The required fraction = x/y = 6/13

Answer 2

ɢɪᴠᴇɴ :-

A fraction becoms 1/2 if I is added to the numerator and Denominator and it becomes 1/3 when 1 is subracted from the numerator and 2 is added to Denominator .

ᴛᴏ ғɪɴᴅ :-

• Fraction

Sᴏʟᴜᴛɪᴏɴ :-

➭ Let the fraction be x /y

then,

• ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ 1st ᴄᴏɴᴅɪᴛɪᴏɴs

$\implies \: \frac{x + 1}{y + 1} = \frac{1}{2} \\ \\ \implies \: 2(x + 1) = 1(y + 1) \\ \implies \: 2x + 2 = y + 1 \\ \\ \implies \: 2x - y = - 2 + 1 \\ \\ \implies \: 2x - y = - 1$

We get,

➭ 2x - y = -1

➭ y = (2x +1) ---(1)

Now,

• ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ 2nd ᴄᴏɴᴅɪᴛɪᴏɴ :-

$\implies \: \frac{x - 1}{y + 2} = \frac{1}{3} \\ \\ \implies \: 3(x - 1) = 1(y + 2) \\ \\ \implies \: 3x - 3 = y + 2 \\ \\ \implies \: 3x - y = 2 + 3 \\ \\ \implies \: 3x - y = 5$

We get,

➭ 3x - y = 5. --(2)

Put the value of (1) in (2) , We get,

➭ 3x - (2x + 1) = 5

➭ 3x - 2x - 1 = 5

➭ x = 5 + 1

➭ x = 6

Put x = 6 in (1) , we get,

➭ y = 2x + 1

➭ y = 2×6 + 1

➭ y = 12 + 1

➭ y = 13

Hence,

• Fraction is x/y = 6/13