Two identical lamps A and B using different types of kerosene can completely utilize the same volume of oil in 12 hours and 8 hours respectively, due to the quality of oil used. If both of them start burning at the same time at their respective constant speed, then after what time does the ratio of the height of kerosene oil left will become 4:3.Â

Given: Two identical lamps A and B using different types of kerosene can completely utilize the same volume of oil in 12 hours and 8 hours respectively.

To find: Here we have to find at what time does the ratio of the height of kerosene oil left will become 4:3.

Solution:

Assuming Shape of oil tank as cylinder or cuboid where Volume is directly proportional to height.

Let say volume of oil in both lamps = 24a

Let after T hours the ratio of the height of kerosene oil left will become 4 : 3.

Now,

Oil utilize by Lamp A in 12 hrs = 24a

Oil utilize by Lamp A in 1 hr = $\frac{24a}{12}$ = 2a

Oil utilize by Lamp A in T hr  = $2a\ \times\ T$ = 2aT

And,

Oil utilize by Lamp B in 8 hrs = 24a

Oil utilize by Lamp B in 1 hr = $\frac{24a}{8}$ = 3a

Oil utilize by Lamp B in T hrs = $3a\ \times\ T$ = 3aT

After T hours:

Volume remaining in lamp A after T hours = 24a $-$ 2aT

Volume remaining in lamp B after T hours = 24a $-$ 3aT

These, volumes will be in the ratio 4 : 3;

$\frac{24a\ -\ 2aT}{24a\ -\ 3aT}$ = $\frac{4}{3}$

$3(24a\ -\ 2aT)\ =\ 4(24a\ -\ 3aT)$

$72a\ -\ 6aT\ =\ 96a\ -\ 12aT$

$12aT\ -\ 6aT\ =\ 96a\ -\ 72a$

$6aT\ =\ 24a$

T = 4

So, after 4 hrs the ratio of the height of kerosene oil left will become 4 : 3.​

Tutorialspoint

Updated on: 10-Oct-2022

17 Views

Kickstart Your Career

Get certified by completing the course

Get Started