Question

If the numerator of a fraction is increased by 200% and the denominator is increased by 300% the resultant fraction is 11/13. What was the original fraction ?

Answer 1

In the above Question, the following information is given -

The numerator of a fraction is increased by 200% and the denominator is increased by 300%.

The resultant fraction obtained is ( 11 / 13 ).

To find -

Find the required Fraction

Solution -

Let us initially assume that the given fraction is of the form, ( x / y )

Now initially, the numerator of that fraction is increased by 200%.

New Numerator -

=> 200% of x +x

=> ( 200 / 100 ) x +x

=> 2x + x

=> 3x

New denominator -

=> 300% of y + y

=> ( 300 / 100 ) y + y

=> 3y + y

=> 4y

New Fraction -

=> [ New Numerator ] / [ New Denomiator ]

=> [ 2x ] / [ 3y ]

But, the new Fraction is ( 11 / 13 )

So ,

[ 3x / 4y ] = [ 11 / 13 ]

=> [ x / y ] = [ 44 / 39 ]

Thus, the original fraction is ( 44 / 39 ).

This is the required answer.

___________________

Answer 2

✪ Given ✪

• The numerator of a fraction is increased by 200%.
• The denominator is increased by 300%.
• The resultant fraction is 11/13.

✪ To Find ✪

➲ The original fraction.

✪ Solution ✪

Let the numerator of the fraction be x, and the denominator of the fraction be y.

➨ For the numerator (x) :-

→ x is increased by 200 %.

$\sf{\implies Numerator=x+200\%\ of\ x}\\\\\sf{\implies Numerator=x+\dfrac{200}{100}x}\\\\\sf{\implies Numerator= x+\dfrac{200x}{100}}\\\\\sf{\implies Numerator= x+2x}\\\\\sf{\implies Numerator=3x}$

$\rule{170}2$

➨ For the denominator (y) :-

→ y is increased by 300 %.

$\sf{\implies Denominator = y+300\%\ of\ y}\\\\\sf{\implies Denominator = y+\dfrac{300}{100}y}\\\\\sf{\implies Denominator = y+\dfrac{300y}{100}}\\\\\sf{\implies Denominator = y+3y}\\\\\sf{\implies Denominator = 4y}$

$\rule{170}2$

A/q,

After x and y were increased by 200% and 300% respectively, the resultant fraction was 11/13. We get :-

$\sf{\dfrac{3x}{4y}=\dfrac{11}{13}}\\\\\sf{\implies 39x=44y}\\\\\sf{\implies \dfrac{39x}{y}=44}\\\\\boxed{\sf{\color{lime}{\implies \dfrac{x}{y}=\dfrac{44}{39}}}}$

Therefore, the original fraction was 44/39.