If 20 typists can type 48 letters in 20 minutes, then how many letters

Typist---------------letters--------------time
--20------------------48------------------20
--20-----------------48*3--------------20*3
--1------------------\(\frac{48*3}{20}\)-----------60 min
--30----------------\(\frac{48*3*30}{20-}\)---------60 min

Answer = \(\frac{48*3*30}{20-}=24*3*3 = 216\)
D
_________________

We have given Man ( typists) , Days , Hours ( time ) and Work ( letters ) and two different MAN DAY cases

Then apply simple formula and very important.

M1 D1 H1 / W1 = M2 D2 H2 / W2. ( Ignore days as this is not mentioned in Question ).

Let the unknown work i.e. no of letters be X and 1 hour = 60 mins.

20 * 20 / 48 = 30 * 60 / X.

X = 216.

Option D.

It is always better to find out the time needed for typing one letter in such problems.

Total typist minutes required to type 48 letters = 20*20 = 400 minutes.
Time needed for each letter = 48/400 minutes.

Number of letters completed by 30 typists in 60 minutes = (48/400) * 30*60 = 216 letters.

Correct Option: D

20 typists can type 48 letters, so 30 typists can type = 48*30/20

48*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 48*30*60/20*20= 216

D is the answer
_________________

simple formula of mandays

(20*20)/(60*48) = (30*1)/x

x = 216

20 typist type 48 letters, so 30 typists type = (48/20) * 30 letters in 20 mins.

in 60 mins 30 typists type, = (48/20*20) * 30 * 60 = 216


answer D

20 typists can type 48*20 letter minutes
20*20 typist-minutes is equal to 48 letters
1 typist-minute is equal to 48/(20*20) letters
30*60 typist-minutes is equal to 48*30*60/(20*20) letters =216 letters.

The question is asking about the amount of work done in 60 mins or 1 hours. Using this information we can calculate, the amount of work done by 20 typists in 60 minutes 3 (20)*48 = 144 words. Now we can use the unitary method to find the work done by 30 typists in 60 mins i.e. 144/20*30 = 216 word.

Tip: For a fixed time more men imply more work. (considering work done by each man is consistent) therefore, we can also eliminate answer choice A, B, C.

20 typists can type 48 letters in 20 minutes

So, working at same pace 20 typists can type 48*3 letters in 1 hour (20*3 minutes)
Or, 20 typists can type 144 letters/hr
So, Efficiency per worker is 144/20

If 30 workers are employed , they can produce = 144/20*30 =>216 letters

Answer will be (D)
_________________

48/(20*1/3)=36/5=rate of one typist in one hour
30*36/5=216 letters in one hour

I used ratios
typers:letters:mins
20:48:20
Question asks for one hour
first converted 20 mins into one hour by multiplying by 3
Letter:mins
48(3):20(3)
144:60 mins

then to make the 20 equal to 30 typers i multiplied by 3/2 and also multiplyed 3/2(144)
typers : letters
20(3/2) = 30 typers : 144(3/2) = 216 letters
30 typers: 216 letters

20 machines times their constant respective rate in 20 minutes can produce 48 letters. Therefore, \(20*(r) * 20 = 48,\)
Rate\((r)=\frac{48}{20} * \frac{1}{20} => r= \frac{48}{400}\)

30 machines in 1 hour (60 minutes) will produce how many letters:

\(30 * \frac{48}{400} * 60 = 3*\frac{48}{4}*6 = 18*12=216\)

Option: D

We can set up a proportion to determine the rate n (number of letters per minute) of 30 typists.

20 typists / rate of those 20 typists = 30 typists / (unknown) rate of those 30 typists

20/(48/20) = 30/n

20/(12/5) = 30/n

100/12 = 30/n

100n = 12 x 30

10n = 12 x 3

10n = 36

n = 3.6

We see that the rate of 30 typists is 3.6 letters per minute. So in 60 minutes, 30 typists can complete 3.6 x 60 = 216 letters.

Alternate Solution:

We know that 20 typists can type 48 letters in 20 minutes. Thus, we see that in 60 minutes, or 1 hour, those 20 typists can type 3 times as many letters, or 3 x 48 = 144 letters. We can now set up a proportion for n = the number of letters that can be typed in 1 hour by 30 typists:

20/144 = 30/n

20n = 144 x 30

2n = 144 x 3

n = 216

Answer: D
_________________

For 20 typists, work rate=48/20= 2.4 letters/min
For 1 typist, work rate= 2.4/20 letters/min

For 30 typists, total letters typed in a min=2.4/20*30= 3.6 letters
So, letters typed in 60 mins=60*3.6= 216 letters

(D)

This i how i solved...

20 Typist can type 48 letters / 20 Min therofre in 1 Min 20 Typist can type = 48/20 = 2.4 Letters per Min
In 60 Min 20 Typist can type = 2.4 *60 =144 Words per min...

We are also told now there are 30 Typist so if 20 typist can type 144 words so 30 Typist can type X words per min.....

Solve for X
20/144 = 30 / x .....
x = 72*3 = 216 Words per min

48[letters] = 20[minutes]*(20[typers]/Rate[minutes/letters]) --> Rate = 400/48

X[letters] = 60[minutes*(30[typers]/Rate[minutes/letters]) --> 60[minutes*(30[typers]/(400/48))

X[letters] = 60*30*48/400 = 216