M15-20

Question

Tom read a 480-page book by reading a fixed number of pages each day. If he had read 16 pages more each day, he would have finished the book 5 days earlier. How many days did Tom spend reading the book?

A. 10
B. 12
C. 15
D. 16
E. 18

Show Answer

Official Answer

C

A. 10
B. 12
C. 15
D. 16
E. 18

Bunuel · Accepted Answer

Official Solution:

Tom read a 480-page book by reading a fixed number of pages each day. If he had read 16 pages more each day, he would have finished the book 5 days earlier. How many days did Tom spend reading the book?

A. 10
B. 12
C. 15
D. 16
E. 18

Show Answer

Official Answer

C

A. 10
B. 12
C. 15
D. 16
E. 18

Let's assume that Tom spent  d  days reading the 480-page book. Therefore, he read an average of  \frac{480}{d}  pages per day.
 
If he had increased his reading speed by 16 pages per day, he would have finished the book in  d-5  days, which means he would have read an average of  \frac{480}{d-5}  pages per day.
 
Since we know that the second reading speed is 16 pages per day faster than the first one, we can set up the equation  \frac{480}{d}=\frac{480}{d-5}-16 . At this point, it would be more effective to substitute the answer choices rather than attempting to solve for the value of  d .
 
After testing answer choices, we find that option C, which corresponds to  d=15 , satisfies the equation:  \frac{480}{15}=\frac{480}{15-5}-16 . Therefore, Tom spent 15 days reading the book.

Answer: C

raarun · Answer

Why cant this be solved by the following equation
 \frac{480}{N} -\frac{480}{N+16} =5

stov10 · Answer

A little late to the party but I'll try to answer your question for anyone else facing the same problem Raarun. In the equation above you have  \frac{480}{N}  which represents the number of pages divided by the number of days. Now, you also have  -\frac{480}{N+16} , where you're going wrong is the 16 in the denominator. By increasing the denominator by 16(which is not a unit of days but rather pages per the prompt) here you're going to incorrectly reduce the number of total pages per day in that part of the equation. Hope this helps.

anindame · Answer

Actually the problem CAN be solved this way.

\frac{480}{N} -\frac{480}{N+16} =5 
In the equation above you have  \frac{480}{N} . This represents the total number of pages divided by the number of pages read per day.
Gives the same result.

harsh8686 · Answer

where am wrong?  Bunuel

My method:
Assume that Tom read that book in y days by reading x pages each day.

then yx=480 and (y−5)(x+16)=480
therefore 
⟹ yx = (y−5)(x+16)
⟹ 16y - 5x = 80 ---- equation

now instead of solving further, i am putting in numbers to get the value of y
16y - 5x = 80 
16(5) - 5(0) = 80 ---- this can't be the solution as number of days i.e. x>0
16(10)-5(16) ----- y can be 10
16(15) - 5(32) --- y can be 15 as well

so my method has more than 2 solutions and both are mentioned in the answer choices. Where am wrong?

Bunuel · Answer

You missed that x and y should also satisfy xy = 480. 10 and 15 does not satisfy this.

Shobhit7 · Answer

Testing Answers:

A) days 10: 
pages per day= 48
Increase to 48+16= 64
Now Days taken= 10-5= 5
Product= 64*5 is not 480

B) days 12:
Pages per day= 40
Increase to 40+16= 56
Days taken= 7
56*7 is not 480

C) days 15:
Pages per day 32
Increase to 32+16= 48
Days taken= 10
48*10= 480
Ans C

Posted from my mobile device

sanjay1810 · Answer

Hi  Bunuel ,  chetan2u ,  IanStewart :

Got a silly question but I can't figure it out:
if d is number of days and p is pages read per day, we get d.p = 480 which is clear but finally isn't the question asking for value of d -5 ?
I don't understand why we're finding for d when the question is actually asking for the case when number of days is d-5.
" If  he would have finished the book 5 days earlier by reading 16 pages a day more,  how many days  did Tom spend reading the book?"
Typically,I get these kind of questions wrong because I don't answer for the correct variable.
Please clarify.

Thanks.

Bunuel · Answer

If  he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?

That IF there describes hypothetical salutation. In reality, Tom read a book containing 480 pages by reading the same number of pages each day (the number of days Tom spent reading the book = d).

HWPO · Answer

I got a similar question: I tried to solve this problem, using several equations, all of which didn't work.

I said

\frac{480}{x }  pages = d (days)

Then I said

\frac{480}{(x+16)}  pages = d-5 (days).

I tried to equate these equations but it simply didn't work.

Where did I go wrong here?

Thanks!

Bunuel · Answer

The equations are correct. When you solve you should get x=32 and d=15.

HWPO · Answer

\frac{480}{x}  = d => 480 =   dx

\frac{480}{(x+16)}  pages = d-5 => 480 =   xd-5x+16d-80

xd = xd-5x+16d-80 
 80 = 5x + 16d

How?

Bunuel · Answer

\frac{480}{x } = d

\frac{480}{(x+16)} = d-5   --> substitute d:  \frac{480}{(x+16)}= \frac{480}{x } -5   -->  5 x^2 + 80 x - 7680 = 0  --> x = 32 --> d = 15.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

shivamasthana · Answer

Hey Bunnel,

I was trying to solve the question through this equation

480/x- 480/x+16 = 5. After solving this i get a quadratic eqn x^2 +16x - 1536. And after that, I won't get the same answer. Can you please explain why my equation is wrong or am I making some mistakes in the subsequent steps

Bunuel · Answer

I have no idea! When asking a question, you should really specify your thought process and what variables mean in the equations you get through it. Otherwise, it's hard to decipher and reverse engineer what you might have meant.

shivamasthana · Answer

Okay, will keep that in mind. So basically what I have assumed that
 
X is the number of pages the person reads daily, then 480/x will give us how long it takes the person to read the book. Similarly, 480/x+16 will give us how many days will the person take to read the book if he reads x+16 pages per day.

Also, we have been told that the person takes 5 fewer days when he reads x+16 pages every day.

Hence I have come up with the equation 480/x- 480/x+16 = 5 which after solving came out to be x^2 +16x - 1536. But I am not able to get the correct answer from this.

Bunuel · Answer

You are missing brackets in your equation; it should be 480/x - 480/(x + 16) = 5. Solving this gives x = 32, and thus the number of days would be 480/32 = 15.

SergejK · Answer

when arriving at 80+5p=16d I saw that we can rewrite the equation as 5(16+p)=16d so that 16d must be a multiple of 5, hence d must be a multiple of 5. Seeing that only 15 is a multiple of 5 in the answer choices, 15 must be the answer.

M15-20

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