Exams

Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(i)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(ii)
Solving (i) and (ii), we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.

The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

Time from 7 am to 4.15 pm  = 9 hrs 15 min = 374 hrs 

3 min. 5 sec. of this clock = 3 min. of the correct clock. 

Now 3min.5sec. is37720 hrs of this clock = 3 min.is120 hrs of the correct clock 

374 hrs of clock = 120×72037×374 hrs of the correct clock. 

  = 9 hrs of the correct clock. 

 The correct time is 9 hrs after 7 am. i.e., 4 pm.

Other side = d2-s2= 2254-814 = 1444 = 6 ft

  Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.

Average speed = 2aba+b, here a=25 b=4
= 2 x 25 x 4/(25+4) = 200/29 km/hr.

Distance covered in 5 hours 48 minutes
= Speed x time = (200/29)x (29/5) Distance covered in 5 hours 48 minutes = 40kms.

Distance of the post office from the village = (40/2) = 20 km.