Question

Simple intret on a certain sum for 4 years at 7% p.a. is more then simple interest on the same sum for 2.5 ears at the sume rte by 840. Find the principal amount ?​

Answer 1

Corrected Question :

• Simple interest on a certain sum for 4 years at 7% p.a. is more than simple interest on the same sum for 2.5 years at the same rate by 840. Find the principal amount ?

$~$

Given : Simple interest on a certain sum for 4 years at 7% p.a. is more than simple interest on the same sum of 2.5 years at the same rate by 840.

To Find : The Principal amount ?

______________________

❍ Let's consider the Principal amount be P

$\underline{\frak{As~ we~ know~ that~:}}$

• $\boxed{\sf\pink{Simple~ Interest~ = ~\dfrac{P~×~R~×~T}{100}}}$★

$~$

Solution : Here P is the Principal, R is the Rate of Interest & T is the Time.

$~$

$\underline{\frak{According~ to ~the~ Given ~Question~:}}$

$~$

• Simple Interest on a certain sum of 4 years at 7% p.a. is more than simple interest on the same sum for 2.5 years at the same rate by 840.

$~$

$~~~~~~~~~~{\sf:\implies{1^{st}~Simple Interest~=~2^{nd}~ Simple ~Interest~+~840}}$

$~~~~~~~~~~{\sf:\implies{\dfrac{P~×~7~×~4}{100}~=~\dfrac{P~×~7~×~2.5}{100}~+~840}}$

$~~~~~~~~~~{\sf:\implies{\dfrac{P~×~28}{100}~×~\dfrac{P~×~17.5}{100}~+~840}}$

$~~~~~~~~~~{\sf:\implies{\dfrac{28P}{100}~=~\dfrac{17.5P}{100}~+~840}}$

$~~~~~~~~~~{\sf:\implies{\cancel\dfrac{28P}{100}}}$${\sf{\dfrac{17.5P}{100}~+~840}}$

$~~~~~~~~~~{\sf:\implies{0.28P~=~\dfrac{17.5P}{100}~+~840}}$

$~~~~~~~~~~{\sf:\implies{0.28P~=~\cancel\dfrac{17.5P}{100}}}$${\sf{+~840}}$

$~~~~~~~~~~{\sf:\implies{0.28P~=~0.175P~+~840}}$

$~~~~~~~~~~{\sf:\implies{0.28P~-~0.175P~=~840}}$

$~~~~~~~~~~{\sf:\implies{0.105P~=~840}}$

$~~~~~~~~~~{\sf:\implies{P~=~\dfrac{840}{0.015}}}$

$~~~~~~~~~~{\sf:\implies{P~=~\cancel\dfrac{840}{0.115}}}$

$~~~~~~~~~~{\sf:\implies{P~=~8,000}}$

$~~~~~~~~~~:\implies\underset{\blue{\rm Required\ Answer}}{\underbrace{\boxed{\pink{\frak{P~=~Rs.~8,000}}}}}$

$~$

Hence,

$\therefore\underline{\sf{Principal ~amount ~is~\bf{Rs.~8,000}}}$

$~~~~$$\qquad\quad\therefore\underline{\textsf{\textbf{Hence Verified!}}}$

Answer 2

Here P is the Principal, R is the Rate of Interest & T is the Time.

$~ </p><p></p><p>\underline{\frak{According~ to ~the~ Given ~Question~:}}$

According to the Given Question :

~

Simple Interest on a certain sum of 4 years at 7% p.a. is more than simple interest on the same sum for 2.5 years at the same rate by 840.

~

$~~~~~~~~~~{\sf:\implies{1^{st}~Simple Interest~=~2^{nd}~ Simple ~Interest~+~840}}$

:⟹1

st

SimpleInterest = 2

nd

Simple Interest + 840

$~~~~~~~~~~{\sf:\implies{\dfrac{P~×~7~×~4}{100}~=~\dfrac{P~×~7~×~2.5}{100}~+~840}}$

:⟹

100

P × 7 × 4

=

100

P × 7 × 2.5

+ 840

$~~~~~~~~~~{\sf:\implies{\dfrac{P~×~28}{100}~×~\dfrac{P~×~17.5}{100}~+~840}}$

:⟹

100

P × 28

×

100

P × 17.5

+ 840

$~~~~~~~~~~{\sf:\implies{\dfrac{28P}{100}~=~\dfrac{17.5P}{100}~+~840}}$

:⟹

100

28P

=

100

17.5P

+ 840

$~~~~~~~~~~{\sf:\implies{\cancel\dfrac{28P}{100}}}$

:⟹

100

28P

${\sf{\dfrac{17.5P}{100}~+~840}}$

100

17.5P

+ 840

$~~~~~~~~~~{\sf:\implies{0.28P~=~\dfrac{17.5P}{100}~+~840}}$

:⟹0.28P =

100

17.5P

+ 840

$~~~~~~~~~~{\sf:\implies{0.28P~=~\cancel\dfrac{17.5P}{100}}}$

:⟹0.28P =

100

17.5P

${\sf{+~840}}$

+ 840

$~~~~~~~~~~{\sf:\implies{0.28P~=~0.175P~+~840}}$

:⟹0.28P = 0.175P + 840

$~~~~~~~~~~{\sf:\implies{0.28P~-~0.175P~=~840}}$

:⟹0.28P − 0.175P = 840

$~~~~~~~~~~{\sf:\implies{0.105P~=~840}} :⟹0.105P = 840</p><p>$

$~~~~~~~~~{\sf:\implies{P~=~\dfrac{840}{0.015}}}$

:⟹P =

0.015

840

$~~~~~~~~~~{\sf:\implies{P~=~\cancel\dfrac{840}{0.115}}}$

:⟹P =

0.115

840

$~~~~~~~~~~{\sf:\implies{P~=~8,000}}$

:⟹P = 8,000

$~~~~~~~~~:\implies\underset{\blue{\rm Required\ Answer}}{\underbrace{\boxed{\pink{\frak{P~=~Rs.~8,000}}}}}$

:⟹

Required Answer

P = Rs. 8,000

~

Hence,

$\therefore\underline{\sf{Principal ~amount ~is~\bf{Rs.~8,000}}}∴$

Principal amount is Rs. 8,000

$~~~~ \qquad\quad\therefore\underline{\textsf{\textbf{Hence Verified!}}}$

∴

Hence Verified!