y,z are digits such that p= 0.yzyzyzyz….. q=0.yz r=0.zyzyzy……. If 275p=1+275q, possible value of r-p is/are equal to

note:- first two digit is enough

The answer is 0.27.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Vishal S
Jan 6, 2015

Given that

p=0.yzyzyz... =0. y z \overline{yz}


r=0.zyzyzy... =0. z y \overline{zy}

When we simplify the given equation, we get


\Rightarrow 275(p-q)=1

\Rightarrow 275(0.yzyzyz..-0.yz)=1

\Rightarrow 275(0.00yzyz...)=1

\Rightarrow 0.00yzyz...= 1 275 \frac {1}{275}

By multiplying 100 on both the sides, we get

\Rightarrow 0.00yzyz.. x 100= 1 275 \frac {1}{275} x 100

\Rightarrow 0.yzyz..= 100 275 \frac {100}{275}

\Rightarrow 0.yzyz..=0.3636...

\Rightarrow y=3, z=6

*By substituting y=3 & z=6 in p & r we get *

r-p=0.636363.. - 0.363636......

\Rightarrow r-p=0.2727.. =0. 27 \overline{27}

Therefore the value of r-p=0. 27 \overline{27}

0 pending reports


Problem Loading...

Note Loading...

Set Loading...