A certain sum amounts to ₹ 8640 in 2 years at simple interest and to ₹ 9720 in 3 years. The sum (in ₹) and the rate of interest p.a., respectively, are:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. ₹ 6480 and 16(2/3)%.
Given:
A certain sum amounts to ₹ 8640 in 2 years at simple interest and to ₹ 9720 in 3 years
Formula used:
SI = PRT/100
Amount = P + SI where,
P = principal, R = rate and T = time period
Calculations:
According to the question;
8640 = P + PR/50 ----- (1)
9720 = P + 3PR/100 ----- (2)
Subtract (1) from (2)
1080 = PR/100
PR = 108000
Add (1) and (2), we get
⇒ 18360 = 2P + 5PR/100
⇒ 18360 = 2P + 5 × 1080
⇒ 2P = 18360 - 5400
⇒ P = 6480
Using the values in (1)
⇒ 8640 = P + 2PR/100
⇒ 10800 = 648R
⇒ R = 16(2/3)%