Question

a) Find the amount to be paid at the end of 3 years for Rs.1100 at 11% rate of interest p.a. b) Cost price of an item is Rs.550. It is sold with a profit of 10%. Find the selling price .

Answer 1

Question 1

• Time (t) = 3 years
• Principal (p) = ₹ 1100
• Rate (r) = 11%

$\\ \dag {\boxed{\sf{ Amount_{(A)} = P \left( 1 + \dfrac{r}{100} \right)^n }}}$

Where as:

• n = Time
• p = Principal
• r = Rate

Putting values,

$\colon\implies{\tt{ Amount_{(A)} = 1100 \left( 1 + \dfrac{11}{100} \right)^3 }} \\ \\ \\ \colon\implies{\tt{ Amount_{(A)} = 1100 \left( \dfrac{111}{100} \right)^3 }} \\ \\ \\ \colon\implies{\tt{ Amount_{(A)} = 1100 \times \cancel{ \dfrac{111}{100} } \times \cancel{ \dfrac{111}{100} } \cancel{ \times \dfrac{111}{100} } }} \\ \\ \\ \colon\implies{\tt{ Amount_{(A)} = 1100 \times 1.11 \times 1.11 \times 1.11 }} \\ \\ \\ \colon\implies{\tt\large\red{ Amount_{(A)} = 1504.39 }}$

Hence,

• The Amount of the transaction is ₹ 1504.39

Question 2

• Cost price (cp) = ₹ 550
• Profit (%) = 10%

$\\ \dag {\boxed{\sf{ Selling \ Price _{(sp)} = \left( \dfrac{ Cost \ Price \times (100+Profit_{( \% )} ) }{100} \right) }}}$

According to Question,

$\\ \colon\implies{\tt{ Selling \ Price _{(sp)} = \dfrac{ 550 \times (100+10_{( \% )}) }{100} }} \\ \\ \\ \colon\implies{\tt{ Selling \ Price _{(sp)} = \dfrac{ 55 \cancel{0} \times 11 \cancel{0} }{1 \cancel{00} } }} \\ \\ \\ \colon\implies{\tt{ Selling \ Price _{(sp)} = 55 \times 11 }} \\ \\ \\ \colon\implies{\boxed{\tt\large\pink{ Selling \ Price _{(sp)} = 605 }}}$

Hence,

• The Selling price of an item is ₹ 605