Question

A borrowed amount of 4000 amounts to 5400 in 5 years. How much will 5600 amount
To in 3 years at the same rate? ​

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \text{ \underline{ \:In first case, \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \tt{Principle, P_1 = Rs. 4000} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{Amount , A_1 = Rs. 5400} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{Times, n_1 = 5 \: years} \\ \\ \mathfrak{ \: Suppose, \: } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \text{Rate of interest = r}$

If interest is calculated in Simple Interest, then

$\: \: \: \: \: \: \: \tt{S.I._1 = A_1 - P_1 } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{= Rs. (5400 - 4000) } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{= Rs. 1400}$

$\underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \boxed {\bold{S.I. = \frac{P \times \: r \times \: n }{100} }}$

$\underline{ \bold{ \: \: A.T.Q., \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{1400 = \frac{4000 \times r \times 5}{100} } \\ \\ \tt{ \implies \:140000 = 20000 \times r } \\ \\ \tt{ \implies \:r = \frac{140000}{20000} } \\ \\ \: \: \: \: \: \: \tt{ \therefore \: \: r = 7 \: }$

$\: \: \: \: \: \tt{ \therefore \: Rate \: \: of \: \: interest, \: r = 7\%}$

$\mathfrak{Now,} \\ \\ \underline{ \text{ \: In the second case, \: }} \\ \\ \underline{ \mathfrak{ \: Given, \: }} \\ \\ \: \: \: \: \: \: \: \tt{Principle, P_2 = Rs. 5600} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{Time, n_2 = 3 \: years.} \\ \\ \: \: \: \tt{Rate \: of \: interest, r = 7\%}$

$\underline{ \mathfrak{ \: \: To \: \: find :- \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ Amount , A_2 = ?}$

As interest is calculated under Simple Interest,

$\: \: \: \: \: \: \: \tt{S.I._2 = \frac{P_2 \times r \times n_2 }{100} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ \: = \frac{5600 \times 7 \times 3}{100} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = 1176 \: }$

$\tt {\therefore \: \: Amount, A_2 = P_2 + S.I._2 } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{= Rs. (5600 + 1176)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = Rs. 6776}$

$\therefore \: \: \text{ \red{Rs. 5600} \: will be amounted to \red{Rs. 6776} \: } \\ \text{at the same rate of interest in which } \\ \text{\red{Rs. 4000} \: amounts to \red{Rs. 5400}.}$

Answer 2

Answer:

$\small\underline\textsf{1 \:case \:= \:7\: Rate \:of \:interest }$

$\small\underline\textsf{ 2\: case\: = \:6776 \:Amount }$

$\bf\red{Given}\begin{cases}\tt\blue{Principal= 4000} \\ \tt\orange{Amount=5400} \\\tt\green{Time=5\:years}\\\tt\orange{Rate\: of \:interest = ?}\end{cases}$

$\huge\underline\textsf{Explantion:- }$

$\rightarrow\bf S.I.1 = A1 - P1$

$\rightarrow\bf(5400 - 4000) \\ \rightarrow\bf1440$

$\large\underline\textsf{Formula \:Used }$

$\rightarrow\boxed{\bf S.I = \frac{P \times R \times N}{100}}$

$\large\underline\textsf{A.T.Q }$

$\rightarrow\bf 1400 = \frac{4000 \times R \times 5}{100}$

$\rightarrow\bf r = \frac{\cancel{140000}}{\cancel{20000}}$

$\rightarrow\bf r = 7$

$\large\underline\textsf{Rate \: of \:interest \:=7}$

$\rule{300}{2}$

$\large\underline\textbf{Second\: case }$

$\huge\underline\textsf{Explantion:- 2 }$

$\tt\red{Given}\begin{cases}\sf\green{Principal=5600} \\ \sf\purple{Time=3 \:years} \\\bf\pink{Rate\: of \:interest\: =7} \\ \tt{Amount=?}\end{cases}$

$\boxed{\bf S.I.2 = P \times R \times N}$

$\boxed{\bf \frac{56\cancel0\cancel0 \times 7 \times 3}{1\cancel0\cancel0} } \\ \boxed{\bf{\red{= 1176}}}$

$\rule{300}{2}$

$\large\underline\textsf{Amount:- }$

$\rightarrow\bf p2 + s.i.2$

$\rightarrow\bf (5600 + 1176)$

$\rightarrow\bf amount = 6776$

$\small\underline\textsf{1 \:case \:= \:7\: Rate \:of \:interest }$

$\small\underline\textsf{ 2\: case\: = \:6776 \:Amount }$