Let the principal be P and rate be r%.Then
2P = P(1 + r/100)⁵
⇒ (1 + r/100)⁵ = 2
Let it be 8 times in t years, then
∵ 8P = P(1 + r/100)^t

Correct Option: A

Let the principal be P and rate be r%.Then
2P = P(1 + r/100)⁵
⇒ (1 + r/100)⁵ = 2
Let it be 8 times in t years, then
∵ 8P = P(1 + r/100)^t
⇒ (1 + r/100)^t = 8
⇒ (2)³ ⇒ (1 + r/100)¹⁵
∴ t =15 year.

Let the principal be P. Then,
∵ P(1 +10/100)² - P =420
⇒ P(121 - 100/100) =420
⇒ P = Rs. 2000

Correct Option: D

Let the principal be P. Then,
∵ P(1 +10/100)² - P =420
⇒ P(121 - 100/100) =420
⇒ P = Rs. 2000
∴ Requared S.I.= Rs.(2000 x 2 x 10)/100
= Rs. 400

1600(1 +5/100)^t = 1944.81
⇒ (21/20)^t =194481/160000 =(441/400)² = (21/20)⁴
∴ T = 4( half years)
⇒ Required time =2 years

Correct Option: A

1600(1 +5/100)^t = 1944.81
⇒ (21/20)^t =194481/160000 =(441/400)² = (21/20)⁴
∴ T = 4( half years)
⇒ Required time =2 years

Compound interest = P {(1 + r/100)^t - 1}
= 10105 { (1 +10/100)³ - 1}

Correct Option: C

Compound interest = P {(1 + r/100)^t - 1}
= 10105 { (1 +10/100)³ - 1}
=10105 {(11/10)³ - 1}
=10105 {1331/1000 - 1}
=10105(331/1000)
= 3344.755
= Rs. 3300(app.)

From question it is clear that the simple interest of rupees 225 for one year is 238.50 - 225.

Correct Option: B

From question it is clear that the simple interest of rupees 225 for one year is 238.50 - 225.
So Rate = (simple interest x 100 )/( time x principle)
= {(238.50 - 225) x 100}/(225 x 1) % = 6%