mixing problem

[narainash25]

Hi!!Explain the following problems r least post u r thoughs coz itz very important and very urgent!!

1. From a vessel, 1/3rd of the liquid evaporates on
the first day.
On the second day 3/4th of the remaining liquid
evaporates.
What fraction of the volume is present at the end
of the second day.

Ans: 50%



2. An orange glass has orange juice and white glass
has apple juice both of equal volumes.
50ml of the orange juice is taken and poured into
the apple juice.
50ml from the white glass is poured into the
orange glass.
Of the two quantities, the amount of apple juice
in the orange glass and the amount of orange juice in
the white glass, which one is greater and by how
much?


Ans: The two quantities are equal

A train blows a siren one hour after starting from the station. After that it travels at 3/5th of its speed it reaches the next station 2 hours behind schedule. If it had a problem 50 miles farther from the previous case,it would have reached 40 minutes sooner. Find the distance between the two stations .

[aayushkaistha]

2. An orange glass has orange juice and white glass
has apple juice both of equal volumes.
50ml of the orange juice is taken and poured into
the apple juice.
50ml from the white glass is poured into the
orange glass.
Of the two quantities, the amount of apple juice
in the orange glass and the amount of orange juice in
the white glass, which one is greater and by how
much?

let total volume of each liquid be v.
50 ml from orange juice is taken n poured into apple juice.
so, orange juice remaining = v-50

total vol in apple juice container = v+50
since, it will form a solution, so quantities of apple n orange juice are uniform throughout.

ie, per unit vol of orange juice = 50/(v+50)
&, per unit vol of apple juice = v/(v+50)

when 50 ml from this container is shifted into orange juice container,
out of the 50 ml,
vol of apple juice transfered = v/(v+50) * 50
= 50v/(v+50) -------------------(i)
vol of orange juice = 50/(v+50) * 50

= 2500/(v+50)


vol of orange juice remaining in apple container = 50 - 2500/(v+50)
= 50v/(v+50) -----------------------(ii)

note closely equations (i) and (ii)....

equation (i) gives us the amount of apple juice we transfered back into orange juice container.

and equation (ii) gives us the amount of orange juice left in the apple juice container...

both are equal.....
Edited by: aayushkaistha

[aayushkaistha]

A train blows a siren one hour after starting from the station. After that it travels at 3/5th of its speed it reaches the next
station 2 hours behind schedule. If it had a problem 50 miles farther
from the previous case,it would have reached 40 minutes sooner. Find
the distance between the two stations


let distance be d


let speed be v


let time that the train would have taken if there was no fault be t





then....


t = d/v ---- (i)





in first case,


traintravels for 1 hr without fault...


dist travelled in 1 hr = v





dist remaining = d - v


speed with which this distance is travelled = 3v/5





time taken to travel (d - v) distance = (d - v) / (3v/5)


total time taken = 1 + (d - v) / (3v/5)





trainreaches 2 hrs late....


hence,





1 + (d - v) / (3v/5) = t + 2





but t = d/v .......... from eq - (i)





=> 1 + (d - v) / (3v/5) = d/v + 2





simplifying this we get..





d = 4v --------- (ii)





in 2nd case....


traintravels 50 miles more without fault...





dist travelled without fault = v + 50


speed with which this dist id travelled = v





=> time taken to travel this dist = (v+50)/v





dist remaining = d - v - 50


speed to travel this dist = 3v/5





=> time taken to travel this dist = (d-v-50) / (3v/5)





total time taken = (v+50)/v + (d-v-50)/(3v/5)





it is given that train reaches 40min (2/3 hrs) earlier...


last time it took time = t+2


so this time time taken = t+2-(2/3)


= t+(4/3)


= (d/v)+(4/3)





=> (v+50)/v + (d-v-50)/(3v/5) = (d/v)+(4/3)





simplifying we get...


2d - 6v = 100





but d = 4v


or v = (d/4)





put value of v...


and we get x = 200 miles


=> v = 50 miles/hr