Answer :

i) Let the fraction is =


According condition (i)


=


= x + 1 = y - 1


= x - y = -2..................(i)


According condition (ii)


=


= 2x = y + 1


= 2x - y = 1..................(ii)


Subtracting equation (i) from equation (ii) we get,


x = 3


Putting value of x in equation (i) we get,


3 - y = -2


= - y = - 5 and y = 5


Hence, the required fraction is


ii) Let present age of Nuri = x


Let present age of Sonu = y


According to condition (i)

five years before Nuri's age is 3 times that of Sonu's age



According to condition (ii)


x + 10 = 2(y + 10)


=


Subtracting equation (i) from equation (ii) we get,


y = 20


Putting value of y in equation (i) we get,


x - 60 = -10


x = 50


Hence,


Present age of Nuri = 50 years


Present age of Sonu = 20 years


iii) Let the unit digit of number = x


Let tens digit = y


so number = 10y + x


Number formed after reversing the digits = 10x + y


According to the question,


x + y = 9 ...................(i)


9(10y + x) = 2(10x + y)


= 90y + 9x = 20x + 2y


= 88y -11x = 0


= - x + 8y = 0..................(ii)


Adding equations (i) and (ii). we get,


9y = 9


= y =


Putting value of y in equation (i), we get,


x = 8


Hence,


The required number is = 10y + x = 10×1+8 = 18


iv) Let the number of Rs, 50 notes = x


Let the number of Rs, 100 notes = y


According to the question,


x + y = 25 ......................(i)


50x + 100y = 2000...............(ii)


Multiplying equation (i) by 50 we get,


50x + 50y = 1250.................(iii)


Subtracting equation (iii) from equation (ii) . we get,


50 y = 750


= y =


Putting value of y in equation (i) we get,


x = 10


Hence,


Meena has 10 notes of Rs, 50 and 15 notes of Rs, 100.


v) Let the fixed charge for first three days = Rs. x


Let each day charge there after = Rs. y


According to the question,


x + 4y = 27.................(i)


x + 2y = 21 ................(ii)


Subtracting equation (ii) from equation (i) we get,


2y = 6


= y =


Putting value of y in equation (i). we get,


x + 12 = 27


= x = 27 - 12 = 15


Hence,


Fixed charge = Rs. 15


Charge per day = Rs. 3

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