12. Out of Rs. 70,000, I invest Rs. 30,000 at 4% & Rs. 20,000 at 3% S. L. At what rate of interest must I invest the balance to get a return of 5% on whole amount per annum? (b) 7% (c) 8% (d) 8.5% (a) 5%
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Out of Rs. 70,000. I invest Rs. 30,000 at 4% and Rs. 20,000 at 3%, simple Interest. At what rate of interest must I invest the balance so as to get a return of 5% on the whole amount per annum?
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Solution
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Correct option is D)
P
1
=30000
R
1
=4%
T
1
=1
∴S.T
1
=
100
P
1
R
1
T
1
=
100
30000×4×1
=1200
P
2
=20000
R
2
=3%
T
2
=1
S.I
2
=
100
P
2
T
2
R
2
⇒S.I
2
=
100
20000×1×3
=600
P
3
=70000−(30000+20000)
=20000
T
3
=1
R
3
=R(Let)
SI
3
=
100
P
3
T
3
R
3
=
100
20000×1×R
=200R
P
4
=70000
T
4
=1
R
4
=5%
⇒S.I
4
=
100
P
4
R
4
T
4
=
100
70000×5×1
=3500
ATP, S.I
1
+S.I
2
+S.I
3
=S.I
4
⇒1200+600+200R=3500
⇒200R=3500−1800
⇒R=
200
1700
=8.5
Hence the investment must be at 8.5% Rate