A man had 35000. He lent *15000 at 4% p.a. and 10000 at 3% p.a. simple interest. At what rate must he lend the remaining money so that the total income is 5% on 35000 annually?
Answers
Answer:
Solution−
Total Principal Amount, p = Rs 35000
Rate of interest, r = 5 %
Time, t = 1 year
We know,
Income, I on a certain sum of money Rs P invested at the rate of r % per annum for t years is
\boxed{ \tt{ \: I = \frac{p \times r \times t}{100} \: \: }}
I=
100
p×r×t
So, on substituting the values of p, r and t, we get
\rm :\longmapsto\:I = \dfrac{35000 \times 5 \times 1}{100}:⟼I=
100
35000×5×1
\bf\implies \:\boxed{ \tt{ \: I = 1750 \: \: }}⟹
I=1750
Case :- 1
Amount Lent, p = Rs 15000
Rate of interest, r = 4 %
Time, t = 1 year
We know,
Income, I on a certain sum of money Rs P invested at the rate of r % per annum for t years is
\boxed{ \tt{ \: I = \frac{p \times r \times t}{100} \: \: }}
I=
100
p×r×t
So, on substituting the values, we get
\rm :\longmapsto\:I_1 = \dfrac{15000 \times 4 \times 1}{100}:⟼I
1
=
100
15000×4×1
So, on substituting the values, we get
\rm :\longmapsto\:I_1 = \dfrac{15000 \times 4 \times 1}{100}:⟼I
1
=
100
15000×4×1
\bf\implies \:\boxed{ \tt{ \: I_1 = 600 \: \: }}⟹
I
1
=600
Case :- 2
Amount Lent, p = Rs 10000
Rate of interest, r = 3 %
Time, t = 1 year
We know,
Income, I on a certain sum of money Rs P invested at the rate of r % per annum for t years is
\boxed{ \tt{ \: I = \frac{p \times r \times t}{100} \: \: }}
I=
100
p×r×t
So, on substituting the values, we get
\rm :\longmapsto\:I_2 = \dfrac{10000 \times 3 \times 1}{100}:⟼I
2
=
100
10000×3×1
\bf\implies \:\boxed{ \tt{ \: I_2 = 300 \: \: }}⟹
I
2
=300
Case :- 3
Now,
Remaining amount = 35000 - (15000+10000) = 10000
Anount lent, p = Rs 10000
Rate of interest, r = r %
Time, t = 1 year
We know,
Income, I on a certain sum of money Rs P invested at the rate of r % per annum for t years is
\boxed{ \tt{ \: I = \frac{p \times r \times t}{100} \: \: }}
I=
100
p×r×t
\rm :\longmapsto\:I_3 = \dfrac{10000 \times r \times 1}{100}:⟼I
3
=
100
10000×r×1
\bf\implies \:\boxed{ \tt{ \: I_3 = 100r \: \: }}⟹
I
3
=100r
According to statement
\rm :\longmapsto\:I_1 + I_2 + I_3 = I:⟼I
1
+I
2
+I
3
=I
\rm :\longmapsto\:600 + 300 + 100r = 1750:⟼600+300+100r=1750
\rm :\longmapsto\:900 + 100r = 1750:⟼900+100r=1750
\rm :\longmapsto\:100r = 1750 - 900:⟼100r=1750−900
\rm :\longmapsto\:100r = 850:⟼100r=850
\bf\implies \:\boxed{ \tt{ \: r \: = \: 8.5 \: \% \: \: }}⟹
r=8.5%
Answer:
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