Exams

Let the speeds of the car, train and bus be 5x, 9x and 4x km/hr respectively.
Average speed = 5x + 9x + 4x/3 = 18x /3 = 6x km/hr.
Also, 6x = 72 => x = 12 km/hr
Therefore, the average speed of the car and train together is = 5x+9x2= 7x = 7 x 12 = 84 km/hr.

Let the breadth of the given rectangle be x then length is 2x.
thus area of the given rect is 2x2

after dec 5cm from length and inc 5cm breadth , new lenght becomes 2x-5 and breadth is x+5.thus new area =(2x-5)(x+5)=2x2+5x-25

since new area is 75 units greater than original area thus
2x2+75 = 2x+5x-25
5x=75+25
5x=100
therefore x=20
hence length of the rectangle is 40 cm.

Let money invested by Raghu = Rs. x
Money invested by Trishul = 9/10 x = 0.9x
Money invested by Vishal = 9/10x * 110/100 = 0.99x
Also, x+0.9x+0.99x = 5780
= x= 5780/2.89 = 2000

Therefore, amount invested by Raghu is Rs. 2000.

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

=> 35-xx-45 = 11 (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