Two equal sums of money are lent at the same time at 6% and 5% per annum simple interest. The former is recovered 6 months earlier than the latter and the amount in each is Rs. 2300. The sum and the time (respectively) for which the sums of money are lent out are?

Option 1 : Rs. 2,000, 2.5 years and 3 years

We know the formula for calculating Simple Interest.

SI = (P × r × t)/100

Where,

SI = Simple Interest

P = Principle

r = Rate of interest (in percentage)

t = Time period

From the question,

Rate of interests at which sums was lent are

r₁ = 6%, r₂ = 5%

Amount recovered in each case, A = Rs. 2300

Let,

Sums lent be P each.

Time period for sum at 6% = t years

Time period for sum at 5% = (t + 1/2) years (∵ 1 year = 12 months)

So,

P + (P × 6 × t)/100 = 2300

⇒ 100P + 6Pt = 230000   …(1)

Also,

P + /100 = 2300

⇒ 100P + 5Pt + (5/2)P = 230000   …(2)

From (1) and (2),

100P + 6Pt = 100P + 5Pt + (5/2)P

⇒ t = (5/2) years

From (1),

100P + 6P × (5/2) = 230000

⇒ 115P = 230000

⇒ P = Rs. 2000