Quantitative Aptitude - Arithmetic Ability Questions

Given ratio of initial mixture of milk and water in Q = 5 : 3

Let the initial quantity of mixture in vessel Q = 8x

Let quantity of Milk = 5x and

Let quantity of water = 3x

According to the question,

5x + 10 x 353x + 10 x 25 = 85

=> 25x + 30 = 24x + 32

=> x = 2

Required Initial quantity of milk = 5x = 5 x 2 = 10 lit.

(24 + 31 + 18) days = 73 days = 1/5 year .

P = Rs 3000 and R = 18 % p.a.

 S.I=3000*18*15100

Speed of train 1 = 48 kmph
Let the length of train 1 = 2x meter

Speed of train 2 = 42 kmph
Length of train 2 = x meter (because it is half of train 1's length)

Distance = 2x + x = 3x
Relative speed= 48+42 = 90 kmph = (90*5/18)  m/s = 25 m/s 

Time = 12 s

Distance/time = speed 

=>3x/12 = 25 (25*12)/3 

Length of the first train = 2x = 200 meter
Time taken to cross the platform= 45 s

Speed of train 1 = 48 kmph = 480/36 = 40/3 m/s

Distance = 200 + y     [where y is the length of the platform] 

x =100m => 200+y = 45* 40/3
y = 400m

If number of visitors on 1st, 2nd, 3rd, 4th & 5th day are k, l, m, n & o respectively, then
k + l + m + n = 58 x 4 = 232 ---- (i) &
l + m + n + o = 60 x 4 = 240 ---- (ii)
Subtracting (i) from (ii), we get
o-k = 8 ---(iii)
Given, k/o = 8/9 ----(iv)
So from (iii) & (iv), we get
a = 64, e = 72
Therefore, number of visitors on 5th day is 72.

Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m

A's spending 90%                 saving = 10%

B's spending 75%                 saving = 25%

C's spending 60%                 saving = 40%

Let us suppose A, B and C saves Rs. 3.5 and 6 respectively.

 10% of A's saving = Rs.3

100% of A's saving =  = Rs. 30

25% of B's saving = Rs. 5

100% of B's saving =  = Rs. 20

40% of C's saving = Rs.6

100% of C's saving =  = Rs. 15

Divide Rs. 6500 in the ratio of 30 : 20 : 15 as

A's Share  =   = Rs. 3000

B's Share   =  = Rs. 2000

C's Share  =  = Rs. 1500

Let the present ages of Arun and Harish be 4x and 3x years respectively.

Then, 4x + 6 = 26 => x = 5

Harish's age = 3x = 15 years.

Speed =[ 78 x ( 5/18 ) ] m/sec = 65/3 m/sec.

Time = 1 minute = 60 sec.

Let the length of the tunnel be x metres.

Then, [ (800 + x )/ 60 ]= 65/3

3(800 + x) = 3900

 x = 500.