Question

A sum of money becomes 5070 in 18 months and 5610 in 9\2 years. Find the principal,
the rate of interest, and the amount after 5 years.​

Answer 1

$\huge\underbrace\pink{Answer}$

Given :-

⇛Amount after 18 months( A1 ) = ₹5070

⇛Time ( T1 ) = 18 months

⇛1 year = 12 months ( 3/2 years)

⇛Amount after 9/2 years ( A2 ) = ₹5610

⇛Time ( T2 ) = 9/2 years

To Find :-

⇛Simple interest

⇛Principal

⇛Rate of interest

⇛Amount after 5 years

Solution :-

A2 - A1

= ₹5610 - ₹5070

= ₹540

T2 - T1

$= \frac{9}{2} - \frac{3}{2}$

$= \frac{6}{2}$

$= 3 \: years$

∴ Simple interest( SI ) for 3 years = ₹540

SI for 3/2 years = 540/2

= ₹270

Hence, SI for 3/2 years is ₹270

Principal = A1 - SI

= ₹5070 - ₹270

= ₹4800

Hence , The Principal is ₹4800

Now, we will find rate of interest

$\frac{PTR}{100} = 270(SI)$

$\frac{4800 \times \frac{3}{2 } \times r }{100}$

$72r = 270$

$r = \frac{270}{72}$

$r = \frac{15}{4}$

$r = 3.75\%$

Hence, The rate of interest is 3.75%

SI for 5 years :-

$\frac{4800 \times 5 \times 3.75}{100}$

$= 900$

Hence , The simple interest is ₹900

Amount after 5 years = Principal + Simple interest

= 4800 + 900

= ₹5700

Hence , The Amount after 5 years is ₹5700

Answer 2

Given :-

⇛Amount after 18 months( A1 ) = ₹5070

⇛Time ( T1 ) = 18 months

⇛1 year = 12 months ( 3/2 years)

⇛Amount after 9/2 years ( A2 ) = ₹5610

⇛Time ( T2 ) = 9/2 years

To Find :-

⇛Simple interest

⇛Principal

⇛Rate of interest

⇛Amount after 5 years

Solution :-

A2 - A1

= ₹5610 - ₹5070

= ₹540

T2 - T1

= \frac{9}{2} - \frac{3}{2}=

2

9

−

2

3

= \frac{6}{2}=

2

6

= 3 \: years=3years

∴ Simple interest( SI ) for 3 years = ₹540

SI for 3/2 years = 540/2

= ₹270

Hence, SI for 3/2 years is ₹270

Principal = A1 - SI

= ₹5070 - ₹270

= ₹4800

Hence , The Principal is ₹4800

Now, we will find rate of interest

\frac{PTR}{100} = 270(SI)

100

PTR

=270(SI)

\frac{4800 \times \frac{3}{2 } \times r }{100}

100

4800×

2

3

×r

72r = 27072r=270

r = \frac{270}{72}r=

72

270

r = \frac{15}{4}r=

4

15

r = 3.75\%r=3.75%

Hence, The rate of interest is 3.75%

SI for 5 years :-

\frac{4800 \times 5 \times 3.75}{100}

100

4800×5×3.75

= 900=900

Hence , The simple interest is ₹900

Amount after 5 years = Principal + Simple interest

= 4800 + 900

= ₹5700

Hence , The Amount after 5 years is ₹5700