GATE Questions

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(20 x 18) men can complete the work in in one day.

one man's one day work = 1/360

(18 x 15) women can complete the work in 1 day

1 woman's one day work = 1/270

So, required ratio = 1270:1360= 4:3

Here by observing the figure, 

we can complete the above incomplete cube with 2 cubes in 2 rows and 2 columns

=> 2 x 4 = 8.

Hence, with 8 small cubes we can complete the cube.

55 min. spaces are covered in 60 min.

60 min. spaces are covered in min. = min.

Loss in 64 min. = min.

Loss in 24 hrs = min. = min.

Let the ratio amount be 'p'

7p - 3p = 2700

4p = 2700

p = 675

R's Share = 675 × 6 = Rs. 4050

Upto first 5 minutes I, J and K will fill => 5[(1/20)+(1/30)+(1/40)] = 65/120

For next 6 minutes, J and K will fill => 6[(1/30)+(1/40)] = 42/120

So tank filled upto first 11 minutes = (65/120) + (42/120) = 107/120
So remaining tank = 13/120

Now at the moment filling with C and leakage @ 1/60 per minute= (1/40) - (1/70) = 3/280.
So time taken to fill remaining 13/120 tank =(13/120) /(3/280) = 91/6 minutes

Hence total time taken to completely fill the tank = 5 + 6 + 91/6 = 26.16 minutes.

The Dronacharya Award, formally known as Dronacharya Award for Outstanding Coaches in Sports and Games, is sports training honour of the Republic of India. The award is named after Drona, often referred as "Dronacharya" or "Guru Drona", a character from the Sanskrit epic Mahabharata of ancient India.

Let the breadth of floor be 'b' m.

Then, length of the floor is 'l = (b + 25)'

Area of the rectangular floor = l x b = (b + 25) × b

According to the question,

(b + 15) (b + 8) = (b + 25) × b

b2 + 8b + 15b + 120 = b2 + 25b

2b = 120

b = 60 m.

l = b + 25 = 60 + 25 = 85 m.

Area of the floor = 85 × 60 = 5100 sq.m.

The State game of Madhya Pradesh is Mallakhamba.