Given that onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg respectively.
Let’s consider the amount spend on onions in these five months to be 100, 100, 100, 50, 50.
Hence, the number of kgs in these five months should be 10, 5, 4, 2, 1 respectively.
The average expense on onions per kg over these five months is given by

Therefore, the closest average would be 18.

Speed of faster train = 160/12 m/s 
Let's convert it to km/hr = (160/12) x (18/5) = 48 km/hr 
Speed of slower train = 48-6= 42 kmph 
Trains are moving in opposite directions we must add the speeds and convert to m/s 48+42 =
90x5/18 = 25m/s 
(160+x)/14 =25 160 + x = 350 
x = 190m

Let’s consider the total number of pens to be
(100 +x)
Let's consider the fixed-wage of the labour to be ‘w’
case (i): the net profit is 300
CP = 8(100 +x) + w
 SP = 12 x 100 + 11 x = 1200 + 11x 
Profit = SP - CP
300 = 1200 + 11x - 8(100 +x) - w
w - 3x = 100 → eq(1)
Case (ii): the net loss is 300
CP = 8(100 +x) + w
SP = 12 x 100 + 9 x = 1200 + 9x
Loss = CP - SP
300 = 8(100 +x) + w - 1200 - 9x
w - x = 700 → eq(2)

By solving equation (1) & (2) we get w = 1000.
Therefore, the wage of the employee is 1000.
Alternate solution:
We can also do this with a little intuition. The Rs 2 decrease per pen results in 300 loss from the case of 300 profit.
The net value of 600 resulted by selling the remaining pens at Rs 2 lesser.
If the number of remaining pens is x, then 2x = 600

So, x = 300.
Total pens = 100 + 300 = 400.
We can get the wage of an employee(w) by considering profit/loss
Profit = 300
100(12) + 300(11) - 400(8) -w = 300
w = 1000

In a regular hexagon, each internal angle is equal to 120°.
From isosceles triangle ABC, we know the length of two sides and including angle.
We will be able to find the third side (AC) using the Pythagoras theorem or the sine rule.
Hence, AC = 2√3cm
Given that, T is the midpoint.
So, CT = 1cm.
From the right-angled △ ACT,
AC² + CT² = AT²
AT² = (2 √3)² + (1)² = 13
AT = √(13)   

Let's consider the number of patients admitted in hospital A and hospital B to be 'x' and ‘x + 21' 
Given that, the sum of recovery days for patients in hospitals A and B were 200 and 152, respectively.
The average recovery days for patients admitted in hospital A was 3 more than the average in-hospital B.

By solving the above equation we get x = 35.
Hence, the number of patients admitted to hospital A is 35.

Let's consider the one-day earnings of Neeta, Geeta, Sita to be n, g, s respectively.
The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days
n + g = 6(s) → eq(1)
The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days
s + n = 2(g) → eq(2)
By solving eq (1) & (2) you will get the ratio n : g : s = 11 : 7 : 3
The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is 11:3