A clock gains 5 seconds in 2 minutes and was set right at 9:00 a.m. If it shows 2:30 in the afternoon on the same day. What is the correct time?
Answer
Given that, the clock gains 5 seconds in 2 minutes $\Rightarrow$ it gains $12 \times 5=60$ seconds i.e. 1 minute in $12 \times 2=24$ minutes $\Rightarrow$ when the incorrect clock moves 25 minutes, the correct clock moves 24 minutes. Now, from 9:00 a.m. to 2:30 p.m. on the same day the time passed by incorrect clock $=5$ hours 30 minutes $=330$ minutes. When an incorrect clock moves 330 minutes, the correct clock moves $=\frac{24}{25} \times 330$ minutes $=316$ minutes 48 seconds $=5$ hours 16 minutes 48 seconds Hence, the correct time is 2:6:48 p.m.
If RAHUL is coded as 22-5-12-25-16, then how will you code VIRAT?
Answer
Here R is coded as 22 which is its actual positions $18+4$. Similarly, A is coded as $1+4$ i.e. 5 . H is coded as $8+4=12$, U is coded as $21+4=25$ and L is coded as $12+4=16$. V is equivalent to $22+4=26$ I is equivalent to $9+4=13$ $R$ is equivalent to $18+4=22$ A is equivalent to $1+4=5$ and T is equivalent to $20+4=24$ $\therefore$ 'VIRAT' will be coded as 26-13-22-5-24
A and $B$ together can build a wall in 30 days. If $A$ is twice as good a workman as $B$, in how many days will $A$ alone finish the work?
Answer
Since A is twice as good a workman as B, A's one day work = B's 2 days work $\Rightarrow$ B's one day work = A's $\frac{1}{2}$ day work ..(i) Since A and B together can build a wall in 30 days, $\therefore$ A's one day work + B's one day work $=\frac{1}{30}$ $\Rightarrow$ A's one day work + A's $\frac{1}{2}$ day work $=\frac{1}{30}$ [using (i)] $\Rightarrow$ A's $1+\frac{1}{2}$ i.e. $\frac{3}{2}$ days work $=\frac{1}{30}$ $\Rightarrow$ A's one day work $=\frac{2}{3} \times \frac{1}{30}=\frac{1}{45}$ $\therefore$ An alone can complete the work in 45 days.
