P and Q are 27 km away. Two trains will having speeds of 24 km/h and 18 km/h respectively starts simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is

area of theplot = 110 * 65 = 7150 sq.m
area of the plot excluding the path = (110-5)* (65-5) = 6300 sq.m
area of the path = 7150 - 6300 =850 sq.m
cost of gravelling the path = 850 x (80/100) = 680 Rs

area of the plot = 120m x 60m = 7200 sq.m
area of plot excluding gravel = 117m x 57m = 6669 sq.m
area of gravel = 7200 sq.m - 6669 sq.m = 531 sq.m
cost of building it = 531 sq.m x 65 ps = 34515 ps
In Rs. = 34515/100 = Rs. 345.15.

Let there be x pupils in the class.

Total increase in marks = (x * 1/2) = x/2.

x/2 = (83 - 63) => x/2 = 20 => x = 40.

Quantity of fruit juice in the mixture = 70 - [70 x (10/100) ]= 63 litres.

After adding water, juice would form 87.5% of the mixture.

Hence, if quantity of mixture after adding x liters of water, [(87.5) /100 ]*x = 63 => x = 72 

Hence 72 - 70 = 2 litres of water must be added.

Correct Sum = (36 * 50 + 48 - 23) = 1825.

Correct mean = = 1825/50 = 36.5

Ratio of Milk and water in a vessel A is 4 : 1

Ratio of Milk and water in a vessel B is 3 : 2

Ratio of only milk in vessel A = 4 : 5

Ratio of only milk in vessel B = 3 : 5

Let 'x' be the quantity of milk in vessel C

Now as equal quantities are taken out from both vessels A & B

=> 4/5     :     3/5
               x 
  3/5-x          x - 4/5

=> 3 5 - x x - 4 5 = 1 1 (equal quantities)

=> x = 7/10

Therefore, quantity of milk in vessel C  = 7

=> Water quantity = 10 - 7 = 3

Hence the ratio of milk & water in vessel 3 is 7 : 3 

4 : 2 = 2 : 1

Thus, the two varieties should be mixed in the ratio 2 : 1

Let each side of the square be a. Then, area = . a 2
New side = 125 a 100 = 5 a 4. New area =  5 a 4 2 =  25 a 2 16

Increase in area =  25 a 2 16 - a 2 = 9 a 2 16
Increase% =  9 a 2 16 * 1 a 2 * 100 % = 56.25%.