Q. 24.1( 324 Votes )
Form the pair of
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 ageAccording 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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