SSC GD Constable 4 Feb 2025 Shift 1 Paper

Section: Elementary Mathematics

Question : 42 of 80

Marks: +1, -0

If at same rate of interest, in 2 years, the simple interest is ₹42 and compound interest is ₹51, then what is the principal (in ₹)?

Solution:

\;SI=(P × R × T) \/ 100

\;CI=P(1+R \/ 100)^{T}-P

Calculation:

\;42=(P × R × 2) \/ 100

\;⇒ P R=42 × 50

\;⇒ P R=2100 . . .(1)

\;51=P(1+R \/ 100)^2-P

\;⇒ 51=P [(1+R \/ 100)^2-1]

\;⇒ 51=P [1+2 R \/ 100+(R \/ 100)^2-1]

\;⇒ 51=P [R \/ 50+R^2 \/ 10000]

\;⇒ 510000=P [200 R+R^2]

\;⇒ 510000=200 P R+P R^2 . . .(2)

Substitute (1) in (2):

\;⇒ 510000=200 × 2100+2100 × R

\;⇒ 510000=420000+2100 R

\;⇒ 90000=2100 R

\;⇒ R=90000 \/ 2100

\;⇒ R=300 \/ 7

Substitute R in (1):

\;⇒ P ×(300 \/ 7)=2100

\;⇒ P=2100 ×(7 \/ 300)

\;⇒ P=7 × 7=49

Go to Question:

Prev Question

Next Question