Quiz 1

16/9

Juice remained after 20% is taken out twice=
120*[1 - (20/100)]²=120*(4/5)*(4/5)=76.8 litres.
Quantity of juice taken out=120 - 76.8 = 43.2 litres.

So amount of water mixed=43.2 litres.
Hence ratio of juice and water=76.8/43.2=16/9

2 item cost=900 x 2=1800
discount:6/100 x 1800=108
and 3 item cost=900 x 3=2700
discount:12/100 x 2700 =324
total discount=324+108=432
so y % of (900 x 5)=432 where y is effective discount
y=(432 x 100) /4500 =9.6%(ans)

simple method:
first calculate liquid percentage in remaining solution
i e 36/49*100 =73.5% liquid remaining in solution

let 100l intial soln
100%----------------------------- 73.5%(FINAL)
14.5% -> 85.5%----->;
14.5 % gives 73.5 approx(two times removed)
hence 14.5% is 4 L(because removed liquid is 4L )
100% ?
gives 28 approx

we have to choose random % taken out and try

let x be the initial qty.
after one replacement proportional of milk left x-e/x,
after two (x-e/x)^2,
the ratio is given as 16:9 i.e milk to water ratio,milk would be 16/25
(x-e/x)^=16/25
x-e/x=4/5
1-(e/x)=4/5
1-4/5=e/x
1/5=e/x
x=5E

cow milk = 72 lit.
10 % is milk= 72*10% = 7.2 lit.
condensed milk contains 80 % milk = 7.2 lit.
100 % condensed milk = (7.2/80)*100 = 9 lit.

A+B+C=600
40+(2/5)A=20+(2/7)B=10+(9/17)C. (Given in the question).
On solving both equation we will get A=150 and final answer is 150.

let us say length x
1st mrng x/3
2nd mrng(x/3)*(1/3)=x/9
10% of original height means x/10
3 rd mrng =x/27
so answer 2

A:B:C= 126*3 : 162*5 : 216*4 = 7*3 :9*5 :12*4 =7:15:16

B\'s share = 15/(7+15+16) *570 = 15/38 *570 = 225 rs

let initially mixer=x
A=7x/12 and b=5x/12
and 9 liter drown

A=7(x-9)/12 b=5(x-9)/12
filled with b
b=5(x-9)/12+9
A=7(x-9)/12

now ratio of A and B is 1:2
means b=2A
5(x-9)/12+9=2*7(x-9)/12
9=9(x-9)/12
x=21

ans=21 litre mixer

X_______________|___________________Y
A C B

Let X\'s Speed= a km/h
Y\'s Speed= b km/h
after 1/2 hrs they meet at point C
So..AC= a/2 km (Distance= Speed*Time)
and CB= b/2 km (Distance= Speed*Time)
Now
..X have to cover b/2 km distance to reach B
and
Y have to cover a/2 km distance to reach A
Time
. taken By Y to reached at A = a/2b (Time= Distance (a/2)/ Speed (b))
According to question Time taken by X = 25 minutes + Time taken by Y
i.e. Time taken by X= 25/60 + (a/2b)= (6a+5b)/12b
Now again for X
Speed= Distance/Time
a= (b/2) / (6a+5b)/12b..........Equation (1)
By solving Equation (1) we get a:b = 2:3