A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

Let original length = x and original breadth = y.

Original area = xy.

New length =	x	.
	2

New breadth = 3y.

New area =	❨	x	x 3y	❩	=	3	xy.
		2				2

∴ Increase % =	❨	1	xy x	1	x 100	❩%	= 50%.
		2		xy

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

55 min. spaces are covered in 60 min.

60 min. spaces are covered in	❨	60	x 60	❩min.	= 65	5	min.
		55				11

Loss in 64 min. =	❨	65	5	- 64	❩	=	16	min.
			11				11

Loss in 24 hrs =	❨	16	x	1	x 24 x 60	❩min.	=	32	8	min.
		11		64					11

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.

55 min. spaces gained in 60 min.

45 min. spaces are gained in	❨	60	x 45	❩min or 49	1	min.
		55			11

∴ The hands are together at 49	1	min. past 9.
	11

Angle traced by hour hand in 12 hrs. = 360°.

Angle traced by it in	11	hrs =	❨	360	x	11	❩	°	= 110°.
	3			12		3

Angle traced by minute hand in 60 min. = 360°.

Angle traced by it in 40 min. =	❨	360	x 40	❩	°	= 240°.
		60

∴ Required angle (240 - 110)° = 130°.

Let breadth = x metres.

Then, length = (x + 20) metres.

Perimeter =	❨	5300	❩	m = 200 m.
		26.50

∴ 2[(x + 20) + x] = 200

⟹ 2x + 20 = 100

⟹ 2x = 80

⟹ x = 40.

Hence, length = x + 20 = 60 m.

Other side	=	❨ 15 ❩ 2 - ❨ 9 ❩ 2 2 2	ft
	=	225 - 81 4 4	ft
	=	144 4	ft
	=	6 ft.

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

We have: l = 20 ft and lb = 680 sq. ft.

So, b = 34 ft.

∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.

100 cm is read as 102 cm.

∴ A₁ = (100 x 100) cm² and A₂ (102 x 102) cm².

(A₂ - A₁) = [(102)² - (100)²]

∴ Percentage error =	❨	404	x 100	❩%	= 4.04%
		100 x 100

Let the side of the square(ABCD) be x metres.

Then, AB + BC = 2x metres.

AC = √2x = (1.41x) m.

Saving on 2x metres = (0.59x) m.

Saving % =	❨	0.59x	x 100	❩%	= 30% (approx.)
		2x