Question

a sum of money will amount to rs.5000 in 3years and rs.5500 in 5years. find the sum of money and rate of interest
​

Answer 1

Answer:

• x = Rs. 4250
• r = 5.88%

Given that,

A sum of money 'x' amounts to Rs. 5000 in 3 years and Rs. 5500 in 5 years.

We are required to find the sum of money 'x' and the rate of interest.

Solution:

The formula for calculating Simple Interest is:

$\boxed{S.I. = \dfrac{P\times R\times t}{100}}$

• 'P' refers to the principal amount
• 'R' refers to the rate of interest
• 't' refers to the time period

Substituting according to the given data, we get:

$\implies ( 5000 - x ) = \dfrac{x \times r \times 3}{100} \hspace{20} ...(i)\\\\\\\implies (5500 - x ) = \dfrac{x \times r \times 5}{100} \hspace{20} ...(ii)$

Solving both the equations, we get:

→ ( 5000 - x ) ( 100 ) = 3rx   ...(i)

→ ( 5500 - x ) ( 100 ) = 5rx   ...(ii)

Dividing (i) by (ii) we get:

$\implies \dfrac{(5000-x)}{(5500-x)} = \dfrac{3}{5}\\\\\\\text{Cross multiplying we get,}\\\\\\\implies 5 \times ( 5000 - x ) = 3 \times ( 5500 - x )\\\\\\\implies 25000 - 5x = 16500 - 3x\\\\\\\implies 25000 - 16500 = 5x - 3x\\\\\\\implies 8500 = 2x \\\\\\\implies x = \dfrac{8500}{2} = \boxed{4250}$

Hence the value of 'x' is Rs. 4250.

Substituting value of x in equation (i) we get:

$\implies ( 5000 - 4250 ) = \dfrac{4250 \times r \times 3}{100}\\\\\\\implies r = \dfrac{(5000 - 4250) \times 100}{4250 \times 3}\\\\\\\implies r = \dfrac{750 \times 100}{12750} = \dfrac{75000}{12750}\\\\\\\implies \boxed{r=5.88 \%}$

Hence the value of 'r' is 5.88%.

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

A sum of money will amount to Rupees 5000 in 3 years and Rupees 5500 in 5 years. Find the sum of money and rate of interest.

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Given \: that}}}}$

⚪A sum of money x amount to Rupees 5000 in 3 years and Rupees 5500 in 5 years.

${\bigstar}\large{\boxed{\sf{\pink{To \: find}}}}$

⚪We are required to find the sum of money x and the rate of interest.

${\bigstar}\large{\boxed{\sf{\pink{Solution}}}}$

${\color{purple}{\mathtt{\large{Formula \: of \: calculating \: SI}}}}$

Simple Interest ☞

Principal × Rate × Time / 100

• We write Principal as P also.
• We write Time as T also.
• We write Rate as R also.

Substituting according to the given data we get,

Solving both the equation we get,

⚫( 5000 - x ) ( 100 ) = 3rx

⚫( 5500 - x ) ( 100 ) = 5rx

Dividing 1 and 2 we get,

• ( 5000 - x ) / ( 5500 - x ) = 3 / 5

By Cross multiplying we get,

• 5 × ( 5000 - x ) = 3 × ( 5500 - x )
• 25000 - 16500 = 5x - 3x
• 8500 = 2x
• x = 8500 / 2
• x = 4250

Hence , the value of x is 4250.

Subsisting value of x in equation 1 we get,

• 5000 - 4250 = 4250 × r × 3 / 100
• R = ( 5000 - 4250 ) × 100 / ( 4250 × 3 )
• R = 750 × 100 / 12750 = 75000 / 12750
• R = 5.88 %

x = 4250

R = 5.88 %

@Itzbeautyqueen23

Hope it's helpful

Thank you :)