Given that, a,b∈0,1,2...9with a+b≠0anda+b10x=a10+b10y=1000. Then, 1x-1y=
1
12
13
14
Explanation for the correct option:
To find the value of 1x-1y:
Givena+b10x=1000 and a10+b100y=1000
Applying logarithm, we get
x=loga+b/101000 and y=loga/10+b/101000
1x=log1000a+b10,1y=log1000a10+b100=log1000110a+b10
⇒1x-1y=log1000a+b10-log1000110a+b10
⇒1x-1y=log100010=log10310⇒1x-1y=13log1010=13
Hence the correct option is C.