Question

At
some rate
of simple
interest, A lent Rs. 6,000 to B
for 2 years and Rs. 1,500 to C
for 4 years and received Rs. 9,00
as interest from both of them
together. The rate of
interest per annum was:
​

Answer 1

Answer:

• The rate of interest per annum was 5%.

Step-by-step explanation:

Given that:

• A lent ₹6000 to B for 2 years.
• A also lent ₹1500 to C for 4 years.
• A receives ₹900 from both of them together.

To Find:

• The rate of interest.

Let us assume:

• The rate of interest be x.

Then,

Simple Interest for B:

$\rm{\longmapsto\dfrac{P\times R\times T}{100}}$

Substituting the values,

$\rm{\longmapsto\dfrac{6000\times x\times 2}{100}}$

Cutting off the zeros,

$\rm{\longmapsto\dfrac{60\!\!\!\not{0}\!\!\!\not{0}\times x\times 2}{1\!\!\!\not{0}\!\!\!\not{0}}}$

$\rm{\longmapsto60\times x\times 2}$

Multiplying the numbers,

$\rm{\longmapsto120x }$

Simple Interest for C:

$\rm{\longmapsto\dfrac{P\times R\times T}{100}}$

Substituting the values,

$\rm{\longmapsto\dfrac{1500\times x\times 4}{100}}$

Cutting off the zeros,

$\rm{\longmapsto\dfrac{15\!\!\!\not{0}\!\!\!\not{0}\times x\times 4}{1\!\!\!\not{0}\!\!\!\not{0}}}$

$\rm{\longmapsto15\times x\times 4}$

Multiplying the numbers,

$\rm{\longmapsto60x }$

Now, according to the question:

$\sf{\longmapsto120x+60x=900}$

Adding the variables,

$\sf{\longmapsto180x=900}$

Transposing 180 from LHS to RHS and changing its sign,

$\sf{\longmapsto x=\dfrac{900}{180}}$

Cutting off the zeros,

$\sf{\longmapsto x=\dfrac{90\!\!\!\not{0}}{18\!\!\!\not{0}}}$

$\sf{\longmapsto x=\dfrac{90}{18}}$

Dividing the numbers,

$\sf{\longmapsto x=5}$

Hence,

• x = 5

Therefore,

• Rate of interest is 5% per annum.