Question

Three sets of English, Hindi and Sociology books dealing with cleanliness have to be stacked in such a way that all books are stored topic wise and the height of each stack is same. The number of English books is 96, the number of Hindi books is 240 and the number of sociology books is 336. (i) Assuming the books are of the same thickness, determine the number of stocks of English, Hindi and Socilogy books.

Answer 1

1.by euclid division lemma
240=96×2+48
96=48×2+0
so the HCF IS 48
no. of stack of the English,hinds,sociology is 48

Answer 2

Answer:

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 HCF Computation of 96, 240 and 336.

\begin{gathered}96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \\ 240 = 2 \times 2 \times 2 \times 2 \times 3 \times 5 \\ 336 = 2 \times 2 \times 2 \times 2 \times 3 \times 7\end{gathered}

96=2×2×2×2×2×3

240=2×2×2×2×3×5

336=2×2×2×2×3×7

Therefore the HCF is 48.

Stacks of English books = 96/48 = 2

Stacks of Hindi books = 240/48 = 5

Stacks of Maths books = 336/48 = 7