Question

Meera’s daughter Ragini was getting married. Her younger daughter Priya was very happy. Meera is 4 times as old as Priya. After 5 years, Meera will be 3 times as old as Priya then. Ragini is 9 years older to Priya. Meera requested her friend Hema to help her by lending Rs 20000. Hema took money from Asif at 12% per annum for 2 years at simple interest. But she gave it to Meera at the same rate and same time but compounded annually. Q1. What profit Hema earned at the end of 2 years? Q2. How old is Ragini? Q3. How much amount Hema paid to Asif?

Answer 1

$\sf\large\underline{Let:}$

$\sf{\implies The\:age\:of\:Meera=x\: years}$

$\sf{\implies The\:age\:of\:Priya=y\: years}$

$\sf{\implies The\:age\:of\: Ragini=y+9\: years}$

$\sf\large\underline{To\: Find:}$

$\sf{\implies The\:age\:of\: Ragini=?}$

$\sf\large\underline{Solution:}$

• By setting up equation and solve the value of x and y]

$\sf\small\underline{Given\:in\: case\:(i):}$

• Meera is 4 times as old as Priya]

$\rm{\implies x=4y-----(i)}$

$\sf\small\underline{Given\:in\: case\:(ii):}$

• After 5 years, Meera will be 3 times as old as Priya]

$\rm{\implies x+5=3(y+5)}$

$\rm{\implies x+5=3y+15}$

$\rm{\implies x-3y=15-5}$

$\rm{\implies x-3y=10------(ii)}$

• In eq (ii) putting the value of x=4y ]

$\rm{\implies x-3y=10}$

$\rm{\implies 4y-3y=10}$

$\rm{\implies y=10}$

$\sf\large{Hence,}$

$\sf{\implies The\:age\:of\:Meera=4y\: years}$

$\bf{\implies The\:age\:of\:Meera=4(10)=40\: years}$

$\sf{\implies The\:age\:of\:Priya=y\: years}$

$\bf{\implies The\:age\:of\:Priya=10\: years}$

$\sf{\implies The\:age\:of\: Ragini=y+9\: years}$

$\bf{\implies The\:age\:of\: Ragini=10+9=19\: years}$

Question 2:

$\sf\large\underline{Given:}$

• Meera requested her friend Hema to help her by lending Rs 20000. Hema took money from Asif at 12% per annum for 2 years at simple interest. But she gave it to Meera at the same rate and same time but compounded annually]

$\sf\large{P=20000\:\:T=2\:\:R=12\%:}$

Calculation for Hema to pay asif after 2 years]

$\tt{\implies SI=\dfrac{P\times\:T\times\:R}{100}}$

$\tt{\implies SI=\dfrac{20000\times\:2\times\:12}{100}}$

$\tt{\implies SI=200\times\:2\times\:12}$

$\tt{\implies SI=4800}$

• Now calculate Amount for Hema to pay asif]

$\tt{\implies Amount=Principal+SI}$

$\tt{\implies Amount=20000+4800}$

$\tt{\implies Amount=24800}$

• Now we focus again in the given Question

$\tt{\implies Given\:in\: question\: again:}$

• But Hema gave it to Meera at the same rate and same time but compounded annually]

Formula used:

$\tt{\implies A=P\bigg(1+\dfrac{r}{100}\bigg)^n}$

$\tt{\implies A=20000\bigg(1+\dfrac{12}{100}\bigg)^2}$

$\tt{\implies A=20000\bigg(\dfrac{112}{100}\bigg)^2}$

$\tt{\implies A=20000\bigg(\dfrac{28}{25}\bigg)^2}$

$\tt{\implies A=20000\times\dfrac{784}{625}}$

$\tt{\implies A=32\times\:784}$

$\tt{\implies A=25088}$

$\sf\large\underline{Answer\: here:}$

Q1. What profit Hema earned at the end of 2 years

To calculate profit earn by Hema we decrease Amount to pay asif and Amount Paid to Hema by Meera

$\sf{\implies Profit\:earn=25088-24800}$

$\sf{\implies Profit\:earn=288}$

Q2. How old is Ragini?

$\rm{\implies The\:age\:of\: Ragini=19\: years}$

Q3. How much amount Hema paid to Asif?

$\sf{\implies Amount=24800}$

Answer 2

that is what i call many ques in 1 ques. well sol is provided .. here A' is the amt payable to asif . ...