Quantitative Aptitude - Arithmetic Ability Questions

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they
coincide only once, i.e., at 12 o'clock).

The hands overlap about every 65 minutes, not every 60 minutes.
The hands coincide 22 times in a day.

Now as per question, Karan invested for 12 months and Satish invested for 7 months.

So, Karan:Satish = (29000 x 12):(18000 x 7)

= 348:126

= 58:21

Satish Ratio in profit will be= 16970×2179 = Rs. 4511

The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.

Frequency of step of A:B:C = 5 : 6 : 7

But in terms of size of step, 6A = 7B = 8C

Therefore, Ratio of speeds of A, B and C = 5/6 : 6/7 : 7/8 = 140 : 144 : 147

Let the present ages of Mahesh, Nilesh and Ramesh be k, l and m respectively.
k/l = 5/x ------ (1)
k = m - 18 ------ (2)
m + 9 = 47 ------ (3)
k - l = m ----- (4)
(3) => m = 47 - 9 = 38 years
(2) => k = 38 -18 = 20 years
(1) => 20/l = 5/x => l = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5

Area of the sheet = 20×30cm2  

Area used for typing = 20-4×30-6cm2   

required % =384600×100=64%

Relative speed = (120 + 80) km/hr

=(200*5/18)m/s = (500/9)m/s

Let the length of the other train be x metres.

Then, x+270/9 = 500/9 

=>  x + 270 = 500

=>  x = 230.

For ticking 6 times, there are 5 intervals.

Each interval has time duration of 30/5 = 6 secs

At 12 o'clock, there are 11 intervals,
so total time for 11 intervals = 11 x 6 = 66 secs.