Question

$\mathtt{\large\underline \pink{Question : - } }$
Reena borrowed from kamal a certain sum for two years at simple interest. Reena lent this sum to hamid at the same rate fir 2 years. At the end of 2 years she recieved rs 110 as compound interest and paid rs 100 as simple interest. find the sum and rate of interest.

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Answer 1

Answer:

Rs 250 and 20%

Simple interest for two years= Rs. 100

∴Interest per year=Rs.50

By compound interest

Interest for I year=Rs.50

Interest for II year=Rs.(110−50)=Rs.60

=50+20% of 50=Rs.60

∴Rate of interest=20%

Let sum borrowed by Reena be P

⇒S.I=

100

PTR

⇒100=

100

P×2×20

⇒P=

2×20

100×100

⇒P=250

∴Sum borrowed=Rs.250

Rate of interest=20%

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Answer 2

Question:-

Reena borrowed from Kamila certain sum for two years at simple interest Reena lent this to Hamid at the same rate for two years compound interest. At the end of two years she received Rs 110 as compound interest but paid Rs 100 as simple interest

To Find:-

Sum and rate of interest.

$\qquad \longrightarrow\underline{ \boxed{ \sf \purple{Solution:- }}}$

Formula:-

$\purple{{ \sf \: CI = P \bigg \{ { \bigg(1 + \frac{R}{100} \bigg) }^{n} - 1 \bigg \}}} \\ \\ \rm \: And\\ \\ \bf \red{SI = \frac{P \times R \times \: T} {100} }$

So,

$\rm \: SI = \frac{PRT}{100} \\ \\ \dashrightarrow \rm \: 100 = \frac{PR \times 2}{100} \\ \\ \dashrightarrow \rm \: PR = \frac{100 \times \cancel{100}}{ \cancel2} \\ \\ \dashrightarrow \rm \underline{ \purple{\boxed{ {{ \sf \: PR = 5000}}}}}$

Also,

$\sf \: CI = P \bigg \{ { \bigg(1 + \frac{R}{100} \bigg) }^{n} - 1 \bigg \} \\ \\ \longrightarrow \sf \: 110 = P \bigg \{ { \bigg(1 + \frac{R}{100} \bigg) }^{2} - 1 \bigg \} \\ \\ \longrightarrow \sf \: 110 = P \bigg \{ \: \cancel1 + \frac{ \cancel2R}{ \cancel{100}} + \frac{ {R}^{2} }{10000} - \cancel1 \bigg \} \\ \\ \longrightarrow \sf \: 110 = P \bigg \{ \: \frac{R}{50} + \frac{ {R}^{2} }{10000} \bigg \} \\ \\ \longrightarrow \sf \: 110 = \frac{PR}{50} + \frac{PR}{10000} \times R \\ \\ \longrightarrow \sf \: 110 = \frac{5000}{50} + \frac{5000}{10000} \times R \\ \\ \sf \: \longrightarrow \: 110 = 100 + \frac{R}{2} \\ \\ \longrightarrow \sf\: \frac{R}{2} = 110 - 100 \\ \\ \longrightarrow \sf \: \frac{R}{2} = 10 \\ \\ \sf \:\longrightarrow\underline{\boxed{\purple{\sf R = 20}}}$

Now we get R as 20%

So,

• PR = 5000

• $\qquad \sf \: S=\frac{5000}{2}$

• Sum = Rs. 250

Answer

• Sum = Rs. 250

• Rate% = 20%