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baburam

· started a discussion

· 1 Months ago

babu (Question: 110369.0 )

3/5

Question:
The sum of the numberator and denominator of certain fraction is 8. If 2 is added to both the numerator and the denominator the value of the fraction increased by \(\cfrac{4}{35}\), then the fraction is:
Options:
A) \(\cfrac{1}{7}\)
B) \(\cfrac{3}{5}\)
C) \(\cfrac{5}{3}\)
D) Can not be determinted
Solution:
Ans: (b) Let fraction be \(\cfrac{x}{y}\)

by given condition

x + y = 8                       .............. (i)

and \(\cfrac{x+ 2}{y+2}-\cfrac{x}{y}=\cfrac{4}{35}\)

or \(\cfrac{2x+ 2y-xy-2x}{y(y+2)}=\cfrac{4}{35}\)

or \(\cfrac{2(y-x)}{y(y+2)}=\cfrac{4}{35}\)

or 35 (y - x) = 2y (y + 2)   .......... (ii)

from (i)

x = 8 - y

substituting this value in (ii)

35 (y - 8 + y) - 2y (y + 2)

35 (y - 4) = y (y + 2)

y2 - 33y + 140 = 0

y= 28 or 5

We cant take 28, taking y=5, x will become 3

Therefore x/y = 3/5

Knowledge Expert

· commented

· 1 Months ago

Two values of a and b are possible
a(-20,3)
b(28,5)
So we have two fractions of which one is negative and other is positive
a/b=-5/7 or 3/5
Of which we have 3/5 in our options as option(b)
Thanks and Regards
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