Question

I have Rs.3500 and lend Rs.1500 at 4% and Rs.1000 at 3%. At what rate must I lend the remainder of my money so that my total income may be 5% on Rs.3500 ?
(Please help me!!! urgent)

Answer 1

Answer:

8.5 %

Step-by-step explanation:

Total income = 5% of Rs.3500

• ⁵⁄₁₀₀ × Rs.3500
• Rs.175

Interest on the two sums lent

=> 4% of Rs.1500 + 3% of Rs.1000

=> Rs.(⁴⁄₁₀₀ × 1500 + ³⁄₁₀₀ × 1000)

=> Rs.(60 + 30)

=> Rs.90

Balance money = Rs.3500 - (Rs.1500 + Rs.1000)

• Rs.1000

Balance of required interest = Rs.175 - Rs.90 = Rs.85

∴ Rate % per annum = 85 × 100/1000 × 1

• 8.5 %

Answer 2

$\large\underline{\sf{Solution-}}$

Total money = Rs 3500

Ist investment = Rs 1500

Second investment = Rs 1000

So,

Balance = Rs 3500 - Rs 1500 - Rs 1000 = Rs 1000

So,

Amount invested in third investment = Rs 1000

Now,

Rate of interest of first investment = 4 %

Rate of interest of second investment = 3 %

Let the rate of interest of third investment = r %

Now,

We know that,

Income on a certain sum of money of Rs P invested at the rate of r % per annum simple interest for n years is

$\boxed{ \bf{ \: Income = \frac{P \times r \times n}{100}}}$

So,

Income from first investment

$\rm :\longmapsto\:I_1 = \dfrac{1500 \times 4 \times 1}{100} = 60$

Income from Second investment

$\rm :\longmapsto\:I_2 = \dfrac{1000 \times 3 \times 1}{100} = 30$

Income from third investment

$\rm :\longmapsto\:I_3 = \dfrac{1000 \times r \times 1}{100} = 10r$

Income on Rs 3500 at the rate of 5 %

$\rm :\longmapsto\:I = \dfrac{3500 \times 5 \times 1}{100} = 175$

Now, According to statement,

$\rm :\longmapsto\:I_1 + I_2 + I_3 = I$

On substituting the values, we get

$\rm :\longmapsto\:60 + 30 + 10r = 175$

$\rm :\longmapsto\:90 + 10r = 175$

$\rm :\longmapsto\:10r = 175 - 90$

$\rm :\longmapsto\:10r = 85$

$\bf\implies \:r \: = \: 8.5 \: \%$