Question

There is well of depth 30m and frog is at bottom of the well. He jumps 3m in one day and falls back 2m in the same day. How many days will it take for the frog to come out of the well?????

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore No.\:of\:days=28\:days}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about depth of well and the sequence of distance is given.

• We have to find number of days in which frog came out from well.

$\underline \bold{Given : } \\ \implies Depth \: of \: well( a_{n}) = 30 \: m \\ \\ \implies First \: step (a)= 3m \\ \\ \implies Difference(d) = 1 \\ \\ \implies Sequence(A.P) = 3,4,5,...... \\ \\ \underline\bold{To \: Find : } \\ \implies No. \: of \: days(n) = ?$

• According to given question.

$\bold{By \: Using \: n_{th} \: term \: Formula : } \\ \implies a_{n} = a + (n - 1) \times d \\ \\ \implies 30 = 3 + (n - 1) \times 1 \\ \\ \implies 30 - 3 = n - 1 \\ \\ \implies 27 + 1 = n \\ \\ \bold{\implies n = 28} \\ \\ \bold{\therefore After \: 28 \: days \: frog \:will\: came \: out}$

Answer 2

Answer:

28 days

Step-by-step explanation:

It is given that the distance climbed by the frog during daytime=3m

The distance by which the frog falls during night=2m

Therefore,

the effective distance covered by the frog in a day

=the distance climbed by the frog during daytime - The distance by which the frog falls during night

=3m-2m=1m

Thus, effectively the frog takes one day to climb one meter. Therefore, it should take 27×1 days to climb up 27m……………………(1.1)

However, on the 28th day, once the frog climbs up 3m in the daytime, it will get out of the well……….(1.2)

Therefore, from (1.1) and (1.2), we see that the number of days required for the frog to get out of the well = Time taken to climb 27m+ 1 day to ascend 3m during daytime

=27days+1 day=28days

Thus, the required answer is 28 days.

Note: We should not consider that the effective length travelled by the frog on all days is 1m because it just needs to reach the top of the well, which it does on the daytime of 28th day. Therefore, after the 28th day’s daytime, we should not consider that it would fall 2m again at night as it would have already gone out.