Question

a sum of 44200 is divided between John and smith , 12 year old and 16 year old respectively, in such a way that if their portions be invested at 10% per annum compound interest, they will receive equal amounts of on reaching 16 years of age. (1)what is the share of each out of 44200. (2)what will each receive when 16 year old.

Answer 1

$\rm\red{Correct~ question:-}$

A sum of 44200 is divided between John and smith , 12 year old and 14 year old respectively, in such a way that if their portions be invested at 10% per annum compound interest, they will receive equal amounts of on reaching 16 years of age. (1)what is the share of each out of 44200. (2)what will each receive when 16 year old.

$\huge\sf\orange{Solution}$

Total Sum = Rs44,200

Let the sum ${P}_{1}$ for John = x

And the sum ${P}_{2}$ for Smith = (44200-x)

Rate for both is common

Rate = 10%

Time for John = (16-12) = 4years

Time for Smith = (16-14)

= 2 years

Let the Amount received by John in 4 years = x

and the amount received by Smith = (44200-x)

${P}_{1}=(1+ \dfrac{r}{100})^n = {P}_{2}(1+ \dfrac{r}{100})^n$

Put the given values

$x(1+ \dfrac{10}{100})^4 = (44200-x)(1+ \dfrac{10}{100})^2$

$x(\dfrac{11}{100})^4=(44200-x)(\dfrac{11}{10})^2$

As both the fractions on both sides are same so cut the powers.

 

$x(\dfrac{121}{100}) = 44200-x$

$\dfrac{121x}{100}+x=44200$

$\dfrac{121x+100x}{100}=44200$

$\dfrac{221x}{100}=44200$

$x= \dfrac{44200 \times 100}{221}$

After doing division.

Answer x= Rs20,000

Sum for John = x = Rs20,000

Sum for Smith = (44200-x) = 44,200-20,000)= Rs24,200

(ii) Amount to be received by both.

$A= P(\dfrac{r}{100})^n$

$A= 24200(1+ \dfrac{10}{100})^2$

$A=24200(\dfrac{11}{10})^2$

$24200 \times \dfrac{11}{10} \times \dfrac{11}{10}$

= Rs29,282

______________________________

Some Formulas :-

▪

$sp \: = \dfrac{cp(100 - l\%)}{100}$

This formula is used to find selling price when cost price and loss percent is given.

▪

$cp = \dfrac{(sp \times 100)}{100 + profit\%}$

This formula is used to find cost price when selling price and profit percent is given.

▪

$cp = \dfrac{(sp \times 100)}{100 - loss\%}$

This formula is used to find cost price when loss percent and selling price is given.

▪ Gain = SP - CP

▪ Loss = CP- SP

$gain\% = \dfrac{gain \times 100}{cp}$

▪

$loss\% = \dfrac{loss \times 100}{cp}$

■ Cost price is the price at which an item is bought by the seller.

■ Selling price is the price at which an item is sold by the seller.

Answer 2

AnSwEr

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Age of John =12years

Age of Smith=14years

Let John get =xRs.

⇒ smith get=(44200−x)Rs.

When John will be 16 years old, he will

have money = x(1+ 10/100)²

=x( 11/10)²

When Smith will be 16 years old, he will have

money = (44200−x)[1+ 10/100)²

=(44200−x)( 10/11)²

As both will have same amount

⇒(44200−x)( 10/11)²

=x( 1+10/11)²

⇒44200−x= (121x/100)

⇒44200= (121/100)²

⇒x= (221*44200/100)

=20000 Rs.

⇒ John was given amount =20000Rs.

and Smith get =44200−20000

=24200Rs.