6. A fraction becomes 4/5 when 5 is added to
its numerator and I is subtracted from its
denominator. It becomes 1/2 when 3 and 5
are subtracted from its numerator and
denominator. The numerator of the
fraction will be
(a) 4 (6) 11 (c) 10 (d) 9.
Answers
The numerator of the fraction is 11. Therefore, option (b) is the correct answer.
• Let us consider that the numerator of the fraction is x and the denominator is y.
=> The fraction is x / y .
• According to the first condition :
On adding 5 to the numerator, the numerator becomes x + 5.
On subtracting 1 from the denominator, the denominator becomes y - 1.
• According to the question,
( x + 5 ) / ( y - 1 ) = 4 / 5
Cross-multiplying both sides, we get,
5 ( x + 5 ) = 4 ( y - 1 )
Or, 5x + 25 = 4y - 4
Or, 5x - 4y = - 4 - 25
Or, 5x - 4y = - 29 -(i)
• According to the second condition,
On subtracting 3 from the numerator, the numerator becomes x - 3.
On Subtracting 5 from the denominator, the denominator becomes y - 5.
• According to the question,
( x - 3 ) / ( y - 5 ) = 1 / 2
Cross-multiplying both sides, we get,
2 ( x - 3 ) = 1 ( y - 5 )
Or, 2x - 6 = y - 5
Or, 2x - y = - 5 + 6
Or, 2x - y = 1 -(ii)
• Multiplying equation (ii) with 4, we get,
4 ( 2x - y ) = 4 × 1
Or, 8x - 4y = 4 -(iii)
• Now, subtracting equation (iii) from (i), we get,
5x - (+ 8x ) - 4y - ( - 4y ) = - 29 - ( + 4 )
=> 5x - 8x - 4y + 4y = - 29 - 4
=> - 3x = - 33
=> x = (- 33) / (- 3)
=> x = 11
• Since x is the numerator of the fraction, therefore, the numerator of the fraction is 11.
• The denominator need not be calculated as it is not asked in the question.