Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

Correct Answer: 6%

Explanation:

S.I. = Rs. (15500 - 12500) = Rs. 3000.

Rate =	❨	100 x 3000	❩%	= 6%
		12500 x 4

Correct Answer: 273 m

Explanation:

Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, ∠ACB = 30° and ∠ADB = 45°.

AB	= tan 30° =	1	⟹     AC = AB x √3 = 100√3 m.
AC		√3

AB	= tan 45° = 1     ⟹     AD = AB = 100 m.
AD

∴ CD = (AC + AD)	= (100√3 + 100) m
	= 100(√3 + 1)
	= (100 x 2.73) m
	= 273 m.

Correct Answer: 30°

Explanation:

Let AB be the tree and AC be its shadow.

Let ∠ACB = Θ.

Then,	AC	=	√3     ⟹     cot Θ = √3
	AB

∴ Θ = 30°.

Correct Answer: 173 m

Explanation:

Let AB be the tower.

Then, ∠APB = 30° and AB = 100 m.

AB	= tan 30° =	1
AP		√3

⟹ AP	= (AB x √3) m
	= 100√3 m
	= (100 x 1.73) m
	= 173 m.

Correct Answer: 21.6 m

Explanation:

Let AB be the observer and CD be the tower.

Draw BE ⊥ CD.

Then, CE = AB = 1.6 m,

      BE = AC = 20√3 m.

DE	= tan 30° =	1
BE		√3

⟹ DE =	20√3	m = 20 m.
	√3

∴ CD = CE + DE = (1.6 + 20) m = 21.6 m.

Correct Answer: 4 years

Explanation:

Time =	❨	100 x 81	❩years	= 4 years.
		450 x 4.5

Correct Answer: Rs. 8925

Explanation:

Correct Answer: Rs. 698

Explanation:

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

∴ Principal = Rs. (815 - 117) = Rs. 698.

Correct Answer: 12%

Explanation:

S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.

S.I. for 5 years = Rs.	❨	2205	x 5	❩	= Rs. 3675
		3

∴ Principal = Rs. (9800 - 3675) = Rs. 6125.

Hence, rate =	❨	100 x 3675	❩%	= 12%
		6125 x 5

Correct Answer: Rs. 6400

Explanation:

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x ).

Then,	❨	x x 14 x 2	❩	+	❨	(13900 - x) x 11 x 2	❩	= 3508
		100				100

⟹ 28x - 22x = 350800 - (13900 x 22)

⟹ 6x = 45000

⟹ x = 7500.

So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.