Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
On a certain sum, at the same rate of interest, the simple interest is ₹66 and compound interest is ₹69 for 2 years. What is the sum (in ₹)?
358
356
367
363
358
The interest on interest for the second year is CI−SI=69−66=3. This ₹3 is the interest on the first year's simple interest (₹33) at the same rate. Thus, r=(3/33)×100=9.09%. Apply this to find P.
Simple Interest (SI) for 2 years = ₹66, Compound Interest (CI) for 2 years = ₹69.
Rate(r)=SI2(CI−SI)×100 and Sum(P)=r×TSI×100
The interest on interest for the second year is CI−SI=69−66=3. This ₹3 is the interest on the first year's simple interest (₹33) at the same rate. Thus, r=(3/33)×100=9.09%. Apply this to find P.
Many students mistake the 2-year SI as the interest for only one year; remember that SI is the same for every year, so SI1year=66/2=33.
Calculate SI for one year
Since Simple Interest is uniform for each year, the interest for one year is half of the total simple interest for two years.
SI1yr=266=33
Find the interest earned on interest
The difference between Compound Interest and Simple Interest for two years is the interest earned on the first year's interest.
Diff=CI−SI=69−66=3
Calculate the rate of interest
The interest of ₹3 is earned on the base of ₹33 at the rate 'r' for one year.
r=333×100=11100≈9.09%
Determine the principal sum
Substitute the rate and the 1-year SI into the Simple Interest formula: SI=(P×r×T)/100.
33=100P×(100/11)×1⟹P=33×11=363
D is correct because calculating the rate from the CI-SI difference and substituting it into the SI formula yields the principal sum of ₹363.
This concept is a subset of the 'Successive Percentage' topic; CI−SI for 2 years is equivalent to P×(r/100)2.