Question

A fraction becomes 4/5 if 3 is added to both the numerator and the the denominator . If 5 is added to the numerator and the denomenator , it becomes 5/6, find the fraction

Answer 1

Answer:-

Let the fraction be x/y.

Given:

The fraction becomes 4/5 if 3 is added to both the numerator and denominator.

So, (x + 3) / (y + 3) = 4/5

After cross multiplication we get,

5(x + 3) = 4(y + 3)

5x + 15 = 4y + 12

5x = 4y + 12 - 15

5x = 4y - 3

x = (4y - 3)/5 -- equation (1)

And,

If 5 is added to both numerator and denominator the fraction becomes 5/6.

→ (x + 5)/(y + 5) = 5/6

→ 6(x + 5) = 5(y + 5)

Substitute "x" value here,

→ 6[ (4y - 3)/5 + 5 ] = 5y + 25

→ 6(4y - 3+25)/5 = 5y + 25

→ 24y + 132 = 25y + 125

→ 132 - 125 = 24y - 25y

→ 7 = y

Substitute "y" value in equation (1)

→ x = 4y - 3/5

→ x = 4(7) - 3/5

→ x = 25/5

→ x = 5

Therefore, the fraction x/y = 5/7.

Answer 2

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$\huge\tt{GIVEN:}$

• A fraction becomes 4/5 if 3 is added to both the numerator and the the denominator .
• 5 is added to the numerator and the denominator

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$\huge\tt{TO~FIND:}$

• the fraction after adding 5 to numerator and the denominator

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$\huge\tt{SOLUTION:}$

Let the fractions be m/n

Now,

➩(m+3)/(n+3) = 4/5

➩5(m+3)=4(n+3)

➩5m + 15 = 4n + 12

➩5m = 4n + 12-15

➩5m = 4n - 3

➩m = (4n -3)/5 ______(EQ.1)

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According to the question,

➩(m+5)/(n+5)=5/6

➩6(m+5)=5(n+5)

➩6[(4n-3)/5+5]=5n+25 (putting the value of m that we got from the (EQ.1))

➩6(4n-3+25)/5=5n+25

➩24n+132=25n+125

➩132-125 = 24n -25n

➩7 = n_________(EQ.2)

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Then,

➩m= 4n -3/5

➩m = 4×7 -3/5(putting the value of n which we got in (EQ.2))

➩m = 25/5

➩m = 5

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