Question

urmila took a loan of rs 850 from rita for 3 years at 8% per annum .after 3 year urmila paid back the loan by giving rs 925 in cash and a new sari. what was the price of the sari?​

Answer 1

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

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \text{Principal, P = Rs. 850} \\ \\ \text{Rate of Interest, r = 8\%} \\ \\ \text{No. of years, n = 3 years} \\ \\ \text{Amount , A = Rs. 925 + A new Saree.} \\ \\ \\ \underline{ \mathfrak{ \: To \: \: find : \mapsto \: \: }} \\ \\ \text{The price of the saree = ?}$

$\underline{ \text{If the interest is calculated on \:Simple Interest}} \:$

$\underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \mathtt{S.I. = \frac{ P \times r \times n}{100} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = \frac{850 \times 8 \times 3}{100} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = \frac{20400}{100} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 204}$

$\text{Hence,} \\ \\ \mathtt{ \therefore \: \: Amount , A = P + S.I.} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = Rs. \: (850 + 204} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = Rs. \: 1054} \\ \\ \\ \underline{ \mathfrak{ \: \: We \: \: have, \: \: }} \\ \\ \: \: \: \: \mathtt{Amount = Rs. 925 + A \: \: new \: \: saree} \\ \\ \mathtt{\Longrightarrow \: Rs. 1054 =Rs. 925 + A \: \: new \: \: saree } \\ \\ \mathtt{\Longrightarrow \: A \: \: new \: \: saree = Rs. 1054 - Rs. 925} \\ \\ \mathtt{\Longrightarrow \: A \: \: new \: \: saree = Rs. \: 129}$

$\bold{Hence,} \\ \: \: \: \: \: \: \: \: \bold{The \: \: price \: \: of \: \: the \: \: saree = Rs. \: 129}$

$\mathfrak{Again,} \\ \\ \underline{ \text{If the interest is calculated Compound annually}}$

$\underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \mathtt{A = P (1 + \frac{r}{100} ) {}^{n} } \\ \\ \: \: \: \mathtt{ = 850 \times (1 + \frac{8}{100}) {}^{3} } \\ \\ \: \: \: \mathtt{ = 850 \times ( \frac{108}{100} ) {}^{3} } \\ \\ \: \: \: \mathtt{ = 850 \times ( \frac{1259712}{1000000}) } \\ \\ \: \: \: \mathtt{ = \frac{1,070,755,200}{1000000} } \\ \\ \: \: \: \mathtt{ =1,070.7552 } \\ \\ \: \: \: \mathtt{ = 1,070.75 \: \: \: \: (approx)}$

$\mathtt{ \therefore \: \: Amount = Rs. \: 1070.75} \\ \\ \underline{ \mathfrak{ \: \: We \: \: have, \: \: }} \\ \\ \: \: \: \: \mathtt{Amount = Rs. 925 + A \: \: new \: \: saree} \\ \\ \mathtt{\Longrightarrow \: Rs. 1070.75 =Rs. 925 + A \: \: new \: \: saree } \\ \\ \mathtt{\Longrightarrow \: A \: \: new \: \: saree = Rs. 1070.75 - Rs. 925} \\ \\ \mathtt{\Longrightarrow \: A \: \: new \: \: saree = Rs. \: 145.75} \:$

$\bold{Hence,} \\ \: \: \: \: \: \: \: \: \bold{The \: \: price \: \: of \: \: the \: \: saree = Rs. \: 145.75}$