# Form the pair of

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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