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Grade 9Magical Mathematics[Interesting Approach]

If n is a positive integer such that n/810=0.d25d25.......

where d is a single digit in decimal base.Find n.

swarali viraj

13 Years agoGrade 9

5 Answers

Chetan Mandayam Nayakar

13 Years ago

USE THE FACT THAT

0.d25d25...=d25(10^(-3) +10^(-6)+...)

=d25(10^-3/(1-10^-3)) by INFINITE GEOMETRIC PROGRESSION

Asan Kumar

13 Years ago

n= 750

swarali viraj

13 Years ago

Could you please explain it ?

swarali viraj

13 Years ago

Can you please explain Mr.Asan Kumar as how you got 75?

Aaryendra Chhabra

9 Years ago

n/810=0.d25d25.... equation 1

multiply both sides by 1000.

therefore, 1000n/810=d25.d25d25d25...... equation 2

equation 2 – equation 1

999n/810=d25

111n/90=d25

n=(d25 x 90)/111

n=(d25 x 30)/37

as written in the question that ‘n’ is a positive integer.

therefore,d25 must be a multiple of 37.

and also ‘d’ is single digit.

therefore, by putting value of ‘d’ from 0 to 9 we get that by putting value of ‘d’ =9.

the condition is satisfied.

therefore, n= (925 x 30)/37

n= 25 x 30

n= 750

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