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A fraction becomes , if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator, it becomes . Find the fraction.
Sol. Let the fraction by 
According to the question

3x + 6 = y + 2
3x – y = 2 – 6
3x – y = –4
3x + 4 = y …(i)

5x + 15 = 2y + 6
5x – 2y = 6 – 15
5x – 2y = – 9
5x – 2(3x + 4) = – 9
…[From (i)
5x – 6x – 8 = – 9
– x = – 9 + 8
– x = – 1
x = 1
From (i), y = 3(1) + 4 = 7
The fraction = = 
Q. 19. Find the middle term of the A.P. 10, 7, 4, …, (– 62) .
Sol. 1 st term, a = 10
Common difference, d = 7 – 10 = – 3
an = – 62
a + (n – 1)d = – 62
10 + (n – 1) (– 3) = – 62
(n – 1) (– 3) = – 62 – 10 = – 72
n – 1 = = 24
n = 24 + 1 = 25
Middle term = term term=13th term
an = a + (n – 1)d a13 = a + 12d
a13 = 10 + 12(– 3) = 10 – 36 = – 26

CBSE 2009 Question Papers Class X
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