Three set of books hindi,mathematics and english have to be stacked in...
Problem
Three sets of books - Hindi, Mathematics, and English - have to be stacked in a way that all the books are stored topic-wise and the height of each stack is the same. The number of Mathematics books is 240, Hindi books are 96, and English books are 336. Assuming that the books are of the same thickness, find the number of stacks of Hindi, Mathematics, and English books.
Solution
Step 1: Find the total number of books
To find the total number of books, we have to add the number of Mathematics, Hindi, and English books.
- Number of Mathematics books = 240
- Number of Hindi books = 96
- Number of English books = 336
Therefore, the total number of books = 240 + 96 + 336 = 672
Step 2: Find the height of each stack
Since the height of each stack is the same, we need to divide the total number of books by the number of stacks.
Let the number of stacks be x.
Therefore, the height of each stack = Total number of books / Number of stacks
Height of each stack = 672 / x
Step 3: Find the number of stacks for each set of books
Hindi Books
Let the number of stacks for Hindi books be y.
Height of each stack = Total number of Hindi books / Number of stacks for Hindi books
96 / y = 672 / x
y = (96*x) / 672
Mathematics Books
Let the number of stacks for Mathematics books be z.
Height of each stack = Total number of Mathematics books / Number of stacks for Mathematics books
240 / z = 672 / x
z = (240*x) / 672
English Books
Let the number of stacks for English books be w.
Height of each stack = Total number of English books / Number of stacks for English books
336 / w = 672 / x
w = (336*x) / 672
Step 4: Find the value of x
Since the height of each stack is the same, y, z, and w should be equal. Therefore,
(96*x) / 672 = (240*x) / 672 = (336*x) / 672
x = 672 / 672 = 1
Step 5: Find the number of stacks for each set of books
Using the value of x, we can find the number of stacks for each set of books.
Hindi Books
y = (96*1) / 672 = 0.