Q9) The ages of two girls are in the ratio 5 : 7. Eight years ago their ages were in the ratio 7 : 13. Find their present ages.  (Marks 2)
Ans9) Let their present ages be 5x and 7x years
8 years ago, their ages were 5x - 8 and 7x - 8 years
According to the question:-
(5x - 8)/(7x - 8) = 7/13
= 65x - 104 = 49x - 55
= 16x = 48
= x = 3
.^.. The present ages of the girls are 15 years and 21 years

Q10) Find the value of k for which the system of equation 8x + 5y = 9, kx + 10y = 15 has no solution.  (Marks 2)
Ans10)  For no solution
a₁/a₂ = b₁/b₂ c₁/c₂
= 8/k = 5/10 9/15
= 5k = 80
= k = 16

Q11) ) Find the G.C.D. of 24(4x² - 9) and 18(2x² + 5x - 12)  (Marks 2)
Ans11)  24(4x² - 9) = 24(2x - 3)(2x - 3)
18(2x² + 5x - 12) = 18(2x - 3)(x + 4)
G.C.D. = 6(2x - 3)
= 12x - 18

Q12) Flow chart. Deleted from the syllabus.  (Marks 2)

Q13) In figure ABCD is a cyclic quadrilateral. AE is drawn parallel to CD and BA is produced. If ABC = 92^o, FAE = 20^o, find BCD.  (Marks 2)

Ans13)  CDA + ABC = 180^o  (sum of opposite angle of cyclic quad. is 180^o)
= CDA + 92^o = 180^o
= CDA = 88^o
AE || CD  (given)
= EAD = CDA  (Alternate interior angles)
= EAD = 88^o
.^.. DAF = 88^o + 20^o = 108^o
But DAF = BCD  (exterior angle of a cyclic quad. is equal to interior opp. angle)
= BCD = 108^o

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