Sumanta needs to type up her 1950-word paper by its 5 pm deadline.

Question

Sumanta needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute. What is the latest time at which Sumanta can begin typing in order to finish her paper by the deadline?

a)2:50 pm
b)3:23 pm
c)3:30 pm
d)4:30 pm
e) 4:42 pm

any experts please explain the solution-how to solve this using backsolving?

A. 2:50 pm
B. 3:23 pm
C. 3:30 pm
D. 4:30 pm
E. 4:42 pm

KarishmaB · Accepted Answer

We will start by assuming the last time:

(E) 4:42 pm
If she starts typing 18 mins before the deadline, she has 18 mins to type 1950 words. Her speed at this time will be 20 + (the mins passed after 3)/2 words i.e. her speed at 4:42 will be
20 + (120 - 18)/2 = 71 words/min
She can type a total of 18 * 71 = 1278 words.
Not enough since she has to type 1950 words. She must start earlier.

(D) 4:30 pm
If she starts 30 mins before deadline, she has 30 mins to type 1950 words. Her speed at this time will be 20 + (120 - 30)/2 = 65 words/min
She can type a total of 30*65 = 1950 words
This is enough.

So she can start at 4:30

Answer (D)

Let's look at the algebraic solution too though backsolving is the best way way here.

Let's say she starts her paper T mins before 5 pm.

Speed = 20 + (120 - T)/2
Time to type = T min

Words typed = 80 - T/2
We need this expression to be not less than 1950

(80 - T/2)*T = 1950
160T - T^2 = 2*1950
T^2 - 160T + 2*1950 = 0
(T - 30)(T - 130) = 0

T can be 30 or 130. The only possible option when two hrs are left is 30 mins.
(Note that if we wouldn't have got integer values for T, it would have become complicated.)

Archit3110 · Answer

VeritasKarishma : I could not understand the meaning of "but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute" what does it mean???

ishpreetanand · Answer

It means that, for example at 3:02pm, the speed will be 21 words/min and at 3:04pm, the speed will be 22 words/min. Basically every 2 minute increment after 3pm increases her speed by 1 word a minute and then remains constant for the entire time she types. Accordingly, for the correct answer (D), when she starts at 4:30pm, her speed is 65 words/min. Here's how it is calculated:

4:30pm - 3pm = 1.5 hour = 90 minutes. There are 45-2 minute interval increments -- 45 + starting speed of 20 words/min at 3pm = 65 words/min.

KarishmaB · Answer

If she starts typing at 3 pm, her constant speed for the next 2 hrs is 20 words/min

If she delays by 2 mins and starts typing at 3:02 pm, her constant speed for the next 1 hr 58 mins is 21 words/min (let's say the anxiety of less time gives her higher speed)

If she delays by another 2 mins and starts typing at 3:04 pm, her constant speed for the next 1 hr 56 mins is 22 words/min (more anxiety, higher speed)

and so on...

Fdambro294 · Answer

Just start from the latest time and see when she can finish the typed report on time.

Every + 2 min after 3 PM ———-> +1 word per minute is added to her original speed of 20 words per minute

1950 words need to be typed

(E) 4 : 42

1 hour and 42 minutes passed = 102 minutes

How many 2 minute skips? 102/2 = 51

For each one of those 52 “skips” she gets +1 added to her original speed of 20 words per minute

So if she starts at 4:42 she will type at (20 + 51) = 71 words per minute

She has 18 minutes until her deadline at 5 : 00

(71) (18) < 1950

She won’t finish it in time if she starts at 4 : 42

(D) 4 : 30

90 minute after start time of 3 PM

90/2 = 45 “skips” of 2 minutes

for each one of these “skips” she’s gets +1 added to her typing Speed of 20 words per minute

So when she starts at 4 :30, her typing speed = (20 + 45) = 65 words per minute

She has 30 minutes to finish the report

(65 word per minute) (30 min) = 1950 words typed

4: 30 is the latest she can start and still finish the report

D

Posted from my mobile device

Kinshook · Answer

sahilkak

Given: Sumanta needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute.
Asked: What is the latest time at which Sumanta can begin typing in order to finish her paper by the deadline?

2x minutes later ; speed = (20 + x) words per minute; Time taken to complete = 1950/(20+x) minutes
The time taken for finish the work = 2x + 1950/(20+x) minutes

2x + 1950/(20+x) = 120
since gap between 3 pm & 5 pm = 2 hours = 120 minutes
2x(20+x) + 1950 = 120(20+x) 
40x + 2x^2 + 1950 = 2400 + 120x
x^2 - 40x - 225 = 0
x^2 - 45x + 5x - 225 = 0
(x-45)(x+5) = 0
x = 45 minutes

Latest time to start = 3pm + 2x minutes = 3 pm + 90 minutes = 4:30 pm

IMO D

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Sumanta needs to type up her 1950-word paper by its 5 pm deadline.

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Sumanta needs to type up her 1950-word paper by its 5 pm deadline.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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