The books for Mathematics, Geography and Science in a school are in the ratio 5:7:8. There is a proposal to increase these books by 40%, 50% and 75% respectively. What will be the ratio of the increased books?
#Please anyone who can help me out with the clearly solution#
original:
number of math books -- 5x
number of geogr books -- 7x
number of science books - 8x
new numbers:
math ----- 1.4(5x) = 7x
geography-- 1.5(7x) = 10.5x
science ----- 1.75(8x) = 14x
new ratio
= 7x : 10.5x : 14x
= 7 : 10.5 : 14
= 14 : 21 : 28
= 2 : 3 : 4
To find the ratio of the increased books, we need to calculate the quantities of the new books for each subject.
Let's start with the existing ratio of the books: 5:7:8.
Step 1: Calculate the increase for each subject.
- Mathematics: Increase by 40%. Therefore, the increase is 40% of 5 books: 0.40 * 5 = 2 books.
- Geography: Increase by 50%. Therefore, the increase is 50% of 7 books: 0.50 * 7 = 3.5 books. Since we cannot have half a book, we'll consider it as 4 books.
- Science: Increase by 75%. Therefore, the increase is 75% of 8 books: 0.75 * 8 = 6 books.
Step 2: Calculate the total quantity of books after the increase.
- Mathematics: There were 5 books initially, and there was an increase of 2 books. So the total quantity of Mathematics books after the increase is 5 + 2 = 7 books.
- Geography: There were 7 books initially, and there was an increase of 4 books. So the total quantity of Geography books after the increase is 7 + 4 = 11 books.
- Science: There were 8 books initially, and there was an increase of 6 books. So the total quantity of Science books after the increase is 8 + 6 = 14 books.
Step 3: Find the ratio of the increased books.
The ratio of the increased books is 7:11:14.
So the final ratio of the increased books is 7:11:14.