Question : A sum of Rs. 6000 is divided into two parts. The annual simple interest on the first part at the annual rate of 10% is equal to the annual simple interest on the second part at the annual rate of 15%. How much is the interest on each part for one year?
Option 1: Rs. 300
Option 2: Rs. 330
Option 3: Rs. 360
Option 4: Rs. 420
Correct Answer: Rs. 360
Solution :
Let the sum be divided into two parts P
1
and P
2
.
Also, let the interest of the two parts be I
1
and I
2
.
For the first part (P
1
):
⇒ I
1
= P
1
× 0.10 × 1 (1 year)
For the second part (P
2
):
⇒ I
2
= P
2
× 0.15 × 1 (1 year)
Now, P
1
× 0.10 × 1 = P
2
× 0.15 × 1
Also, P
1
+ P
2
= 6000
⇒ P
2
= 6000 − P
1
So, P
1
× 0.10 × 1 = (6000−P
1
) × 0.15 × 1
⇒ 0.10P
1
= 0.15(6000−P
1
)
⇒ 0.10P
1
= 0.15(6000−P
1
)
⇒ P
1
= $\frac{900}{0.25}$
⇒ P
1
= Rs. 3600
⇒ P
2
= 6000 − P
1
= 6000 − 3600 = Rs. 2400
⇒ I
2
= P
2
× 0.15 × 1
⇒ I
2
= Rs. 360
Hence, the correct answer is Rs. 360.
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