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. [4 MARKS]

Answer 1

Concept : 1 Mark
Application :1 Mark
Calculation : 2 Marks

We have to find the largest number that divides 96, 240 and 336 exactly. Clearly, such a number is their HCF.

We have,

$96=2^5\times 3$

$240=2^4\times 3\times 5$

$336=2^4\times 3\times 7$

$\therefore$ HCF of 96, 240 and 336 is $2^4\times 3=48$

So, there must be 48 books in each stack

$\therefore$ Number of stacks of English books $=\frac{96}{48}=2$

Number of stacks of Hindi books $=\frac{240}{48}=5$

Number of stacks of Mathematics books $=\frac{336}{48}=7$