A charity organiser is sorting donated books into boxes...

Question

A charity organiser is sorting donated books into boxes. When the total number of books is divided evenly among the boxes, there are 7 books left over. If the division yields a result of 54.14, what is the number of books that each box can hold?

A. 14
B. 42
C. 50
D. 54
E. 61

A. 14
B. 42
C. 50
D. 54
E. 61

Dereno · Answer

Books are being distributed into ‘n’ boxes. The books are evenly distributed among the boxes.

This means, books /n is an integer.

And the remainder is 7.

So, the value of n > 7.

If the quotient is x, then Books = x*n + 7. We are given that the value is 54.14.

The value 54.14 has two parts Integer and decimal part, where the integer is 54 and decimal is 0.14.

Thus, (7/n) = 0.14

n = 7/0.14

= 700/14

= 50

Hence,  n = 50

Option C

ElenaFerrante · Answer

Thank you very much for taking the time to post a solution. Here is my confusion: isn't the question asking for the capacity of each box, whereas n (=50) is the no. of boxes. By that logic, shouldn't the answer be 54? Thank you in advance!

KarishmaB · Answer

54.14 = 54 (14/100) = 54 (7/50)

If our remainder is 7, it means that the divisor must have been 50.
So essentially we split all books into groups of 50 books each and got 54 groups. We were left with 7 books.

So each box had 50 books (and there were 54 boxes)

Ans (C)

Check this video: https://youtu.be/A5abKfUBFSc?si=zAf4SpBDJ7EPfOV0

It explains this concept fully.

ElenaFerrante · Answer

Got it, at last. I invariably turn to your videos for best logic-driven, time-saving approaches. Many thanks!  KarishmaB

Erick1802 · Answer

According to my logic the answer should be 54 i.e option - D:

When a number is divided and gives a decimal result of 54.14, it means:

Each box gets 54 full books

The decimal part (0.14) comes from the remainder

Let the number of boxes be b.

Using remainder form:
Total books = 54b + 7

Using decimal division:
Total books = 54.14b

Equating both:
54.14b = 54b + 7
0.14b = 7
b = 50

So there are 50 boxes, and each box holds 54 books, with 7 books left over.

Answer:
54

Can someone please tell where am I making the mistake because it's saying the answer is 50

Bunuel · Answer

No mistake. The answer should be 54.

There are 2707 books, 50 boxes, each holds 54 books, with 7 left over: 2707/50 = 54.14. Answer D.

Dereno · Answer

Thanks a ton  Erick1802  and  Bunuel . Once again thanks for sharing the solution which helped me understand where I have made the mistake. Nice learning by the way. 👍

Rewriting my solution. As I don’t want to alter the threads and previous posts.

Let’s for time being assume,

Number of books =23

Boxes = 5

23 divided by 5 = quotient 4 and remainder 3.

If the same is represented in decimal form, we get 4.6.

23 = 4 * 5 + 0.6 * 5 = 20 + 3

4  denotes the  number of books per boxes .

Let’s dive to the problem.

Total books / number of boxes = 54.14

Total books = 54 * number of boxes + 0.14 * number of boxes.

Here, 54 denotes the number of books per boxes. ( And NOT NUMBER OF BOXES).

We are given: 0.14 * number of boxes = 7

number of boxes = (7/0.14) = 50.

Total books = 54* 50+7 = 2707.

Option D

Actually, the answer should have been arrived without even solving it.

The questions asks for the number of books per boxes = Integer part of 54.14. And, the decimal part can be utilised for finding the number of boxes. And eventually total books can be found.

A charity organiser is sorting donated books into boxes...

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