A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

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: 9.2 m

Explanation:

Let AB be the wall and BC be the ladder.

Then, ∠ACB = 60° and AC = 4.6 m.

AC	= cos 60° =	1
BC		2

⟹ BC	= 2 x AC
	= (2 x 4.6) m
	= 9.2 m.

Correct Answer: 6

Explanation:

Let rate = R% and time = R years.

Then,	❨	1200 x R x R	❩	= 432
		100

⟹ 12R² = 432

⟹ R² = 36

⟹ R = 6.

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