Question

 A certain sum of money amounts to Rs. 2200 at 5% interest, Rs. 2320 at 8% interest in the same period of time. The period of time is:.

Answer 1

The simple interest formula is

SI = PRT/100

And the amount after time T is given by

Amt = P + SI = P + PRT/100

Amt = P (1 + RT/100)

So, our amount for 5% rate is

2200 = P [ 1 + (5)(T)/100 ]

2200 = P [ 1 + 5T/100 ]

And our amount for 8% rate is

2320 = P [ 1 + (8)(T)/100 ]

2320 = P [ 1 + 8T/100 ]

So, dividing these 2 we get

2200÷2320 = P [ 1 + 5T/100 ] ÷ P [ 1 + 8T/100 ]

55 ÷ 58 = [ 1 + 5T/100 ] ÷ [ 1 + 8T/100 ]

55 ÷ 58 = [ 100 + 5T ] ÷ [ 100 + 8T ]

Cross multiplying, we get

55(100 + 8T) = 58(100 + 5T)

5500 + 440T = 5800 + 290T

150T = 300

T = 2

Therefore, time period is 2 years.

Answer 2

Answer:

different rate =8-5=3%

3%=120

5%=120/3×5

=200

P=2200-200

=2000

T=Si×100/P×R

200×100/2000×5

=2Years ans