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Yogita Ingle 5 years, 8 months ago
let n be any positive integer and b=3
n =3q+r
where q is the quotient and r is the remainder
0_ <r<3
so the remainders may be 0,1 and 2
so n may be in the form of 3q, 3q=1,3q+2
CASE-1
IF N=3q
n+4=3q+4
n+2=3q+2
here n is only divisible by 3
CASE 2
if n = 3q+1
n+4=3q+5
n+2=3q=3
here only n+2 is divisible by 3
CASE 3
IF n=3q+2
n+2=3q+4
n+4=3q+2+4
=3q+6
here only n+4 is divisible by 3
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Posted by Rani Mishra ??? 5 years, 8 months ago
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Yogita Ingle 5 years, 8 months ago
Let the piece of cloth is x metre and it costs Rs.y/metre. Then by the given conditions -
∴, xy=200 -------------(1) and
(x+5)(y-2)=200
or, xy+5y-2x-10=200
or, 200+5y-2x-10=200
or, 5y-2x-10=0
or, 5y=2x+10
or, y=(2x+10)/5
Putting in (1),
x(2x+10)/5=200
or, x(2x+10)=200×5
or, 2x²+10x=1000
or, x²+5x-500=0
or, x²+25x-20x-500=0
or, x(x+25)-20(x+25)=0
or, (x+25)(x-20)=0
either, x+25=0
or, x=-25
or, x-20=0
or, x=20
Since the length of the cloth can not be negative,
∴, x=20 metre
Putting in (1),
20y=200
or, y=10
∴, the cloth is 20 m long and the original rate is Rs. 10/metre.
Posted by Kashish Sarsir 5 years, 8 months ago
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Harshita Talib 5 years, 8 months ago
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