The amount of a certain sum at simple interest at 12.5% p.a. in 5 years is ₹1,725 more than the simple interest on the same sum at the same rate in 10 years. The sum (in ₹) is:
- A4,600
- B5,200
- C4,800
- D4,500
Solution & Step-by-step Explanation
Let the principal sum be P.
Rate of interest (R) = 12.5% p.a.
Case 1:
Time (T
1
) = 5 years
Simple Interest
1
(SI
1
)=
100
P×12.5×5
=0.625P
Amount
1
(A
1
)=P+SI
1
=P+0.625P=1.625P
Case 2:
Time (T
2
) = 10 years
Simple Interest
2
(SI
2
)=
100
P×12.5×10
=1.25P
According to the question, A
1
is ₹1,725 more than SI
2
:
A
1
−SI
2
=1725
1.625P−1.25P=1725
0.375P=1725
P=
0.375
1725
=
8
3
1725
=
3
1725×8
=575×8=4600
Rate of interest (R) = 12.5% p.a.
Case 1:
Time (T
1
) = 5 years
Simple Interest
1
(SI
1
)=
100
P×12.5×5
=0.625P
Amount
1
(A
1
)=P+SI
1
=P+0.625P=1.625P
Case 2:
Time (T
2
) = 10 years
Simple Interest
2
(SI
2
)=
100
P×12.5×10
=1.25P
According to the question, A
1
is ₹1,725 more than SI
2
:
A
1
−SI
2
=1725
1.625P−1.25P=1725
0.375P=1725
P=
0.375
1725
=
8
3
1725
=
3
1725×8
=575×8=4600