Question

Anjali lends a certain amount to Dhruv on simple interest for two years at 20% annual rate of interest. Dhruv gives the entire amount to Diksha on compound interest for two years at the same annual rate. Find the percentage earning of Dhruv at the end of two years on the entire amount.

Answer 1

Answer:

The percentage earning of Dhruv on entire amount is 4%

Step-by-step explanation:

Given that  

 Anjali lends certain amount to Dhruv on simple interest for 2 years at rate of 20% per annum

  Dhruv gave  entire amount to Diksha on compound interest for 2 years at same  annual rate

here we need to find percentage of Dhruv's earning at end of the two years    

let the $P$ be the  certain amount which is given by Anjali ,

Principal amount P = p

time period T = 2 years ( time period is same for both )

rate of interest R= 20% ( rate is same for both )

First find Dhruv's earning

Dhruv's earning will be the subtraction of the amount earn from Diksha and the amount that he need give Anjali  

the total amount that Dhruv need to give Anjali :

total amount = principal amount + interest  

             ⇒ P + $\frac{PTR}{100}$      

             ⇒ p +$\frac{p(2)(20)}{100}$

             ⇒ p +$\frac{2p}{5}$ = $\frac{7}{5} p$  

the amount that Dhruv need give Anjali is  $\frac{7}{5}p$  

The amount earned by Dhruv from Diksha : 

The total amount by compound interest  = principal amount + C.I

                ⇒     P +  [$P[1+ \frac{R}{100}]^{T} -P$ ]

                ⇒    p + $p[1+ \frac{20}{100}]^{2} - p$  

                ⇒   $p( 1+ \frac{1}{5} )^{2}$      

                ⇒ ( $p[\frac{6}{5} ]^{2}$ )

                 ⇒ $\frac{36}{25} p$  

the amount received from Diksha = 36/25 p

the amount earned by Dhruv = $\frac{36}{25} p - \frac{7}{5} p$  

                                                 = $\frac{36p -35p}{25}$ =  $\frac{p}{25}$

the amount he earned   = p/25

percentage of Dhruv's earning =  (p/25)/ p × 100

                                                    = $\frac{p}{25}$ ×$\frac{1}{p}$ ×100

                                                    =     $\frac{1}{25}$ ×100        

                                                     = 4

the percentage of Dhruv's earning = 4%  

Answer 2

Answer:

Step-by-step explanation: