Question

A child attempts to open a five disc-lock. He take 5sec time to dail a particular number on the disc. If he does so for 5hrs everyday, then the number of days he would be sure to open the lock

• A. $30$
• B. $28$
• C. $27$
• D. $25$

Answer 1

The correct option is B $28$

Each disc contains the $digit\mathrm{0...9}(n=10)$
Required number of dailing $=n^r(r=5,asgiven5hrsperday)={10}^5$
$\therefore$ As dailing for each disc $5sec=\frac{5}{60\times 60}hrs.$
$\therefore$ Total time taken for all dailing $=\frac{{10}^5\times 5}{60\times 60}$
Now number of day he would be sure to open the lock.
Number of days $=\frac{{10}^5\times 5}{60\times 60\times 5}=\frac{100\times 1000}{6\times 6\times 100}=\frac{250}{9}=27\frac{7}{9}$ means ${28}^{th}$ will open the lock.