Question

In a library, the ratio of the books on computer, physics and mathematics is 5:7:8. if the collection of books is increased respectively by 40%, 50% and 75%, find out the new ratio

Answer 1

40% increase will lead to a factor of 140 and similiarly 150 and 175.
So new ratio is
(5*140):(7*150):(8*175)
on solving we get 2:3:4

Answer 2

Therefore the required ratio is 2:3:4.

Step-by-step explanation:

Given that, the ratio of books on computer, physics and mathematics is 5:7:8.

Let the number of computer books be 5x.

The  number of physics books be 7x

and the number of mathematics books be 8x.

The number books is increased  respectively by 40%,50% and 75%.

Now, the number of computer books is

$=\textrm{Initial number of books}\times \frac{100+ \textrm{percentage of increase}}{100}$

$=5x\times \frac{100+40}{100}$

$= \frac{5x\times 140}{100}$

Now, the number of physics books is

$=\textrm{Initial number of books}\times \frac{100+ \textrm{percentage of increase}}{100}$

$=7x\times \frac{100+50}{100}$

$= \frac{7x\times 150}{100}$

Now, the number of computer books is

$=\textrm{Initial number of books}\times \frac{100+ \textrm{percentage of increase}}{100}$

$=8x\times \frac{100+75}{100}$

$= \frac{8x\times 175}{100}$

The new ratio of books  on computer, physics and mathematics is

$= \frac{5x\times 140}{100}:\frac{7x\times 150}{100}: \frac{8x\times 175}{100}$

$= 5x\times 140:{7x\times 150}:{8x\times 175}$   [ Multiplying by 100]

$= 5\times 14:{7\times 15}:{4\times 35}$               [dividing by 10x]

$=2:3:4$                                       [dividing by 35]

Therefore the required ratio is 2:3:4.