Quantitative Aptitude – Algebra – if (5.55)^x = (0.555)^y = 1000

Slot – 1 – Quantitative Aptitude – Algebra – if (5.55)^x = (0.555)^y = 1000

if (5.55)^x = (0.555)^y = 1000 – Video

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Q. If (5.55)^x = (0.555)^y = 1000, then the value of 1/x – 1/y is?

1. 2/3
2. 3
3. 1
4. 1/3

Answer: 1/3

Solution: given (5.55)^x = (0.555)^y = 1000 =10^3
Taking log with respect to 10 ( that is base 10)
x log 5.55 = y log (0.555) = 3 log 10 = 3
x log 5.55 = 3
x = 3/log5.55
1/x = log 5.55/3————1)
y log (0.555) = 3
y log (5.55/10) = 3
y log 5.55 – y log 10 = 3
y log 5.55 – y = 3
y = 3 /(log 5.55 -1)
1/y = (log 5.55 -1)/3————-2)
So from eq 1) & 2
1/x -1/y = 1/3

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