Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is the same. The number of English books is 96 , the number of Hindi books is 240 and the number of Mathematics books is 336. Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi and Mathematics books.

Foundation

Mathematics Foundation

HCF and LCM

Question

Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is the same. The number of English books is

96,

the number of Hindi books is

240

and the number of Mathematics books is

336.

Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi and Mathematics books.

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In order to arrange the books as required, we have to find the largest number that divides

96, 240

and

336

exactly. Clearly, such a number is their

H C F

Computation of

H C F

96

and

240

:
Clearly,

H C F

96

and

240

48

.
Computation of

H C F

48

and

336

:
Thus,

H C F

96, 240

and

336

48

.
Hence, there must be

48

books in each stack.
Now, Number of stacks of English books

= \frac{N u m b e r o f E n g l i s h b o o k s}{N u m b e r o f b o o k s i n e a c h s t a c k} = \frac{96}{48} = 2

Number of stacks of Hindi books

= \frac{N u m b e r o f H i n d i b o o k s}{N u m b e r o f b o o k s i n e a c h s t a c k}

= \frac{240}{48} = 5

and, Number of stacks of Mathematics books

= \frac{N u m b e r o f M a t h e m a t i c s b o o k s}{N o . o f b o o k s i n e a c h s t a c k} = \frac{336}{48} = 7