5 Marks Questions

Question 15 Marks

Asha has some money to spare. She wants to deposit ₹ $15000$ for 3 yr in a bank to earn interest. She has two banks to choose from. Bank A gives an interest of 6% per annum compounded annually and Bank B gives $7\%$ per annum simple interest.
Which bank is better choice for depositing ₹ $15000?$ Justify your choice.

Answer

Bank A gives compound interest on ₹ 15000
$=15000\left(\frac{106}{100}\right)^3-15000=$ ₹ $2865.24$
Bank B gives simple interest on ₹ 15000
$=\frac{15000\times7\times3}{100}=$ ₹ $3150$
$\therefore$ So, Bank B is a better choice for depositing ₹ $15000.$

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Question 25 Marks

Living on your own, Sanjay is looking for one bedroom apartment on rent. At Neelgiri apartments, rent for the first two months is $20\%$ off. The one bedroom rate at Neelgiri is ₹ 6000 per month.
At Savana apartments the first month is $50\%$ off. The one bedroom rate at Savana apartments is ₹ $7000$ per month. Which apartment will be cheaper for the first two months and by how much?

Answer

At Neelgiri apartment,
First month rent off $-20 \%$ of 6000 $\quad$ [$20 \%$ off for two months]
$=\frac{20}{100} \times 6000$
$=$ ₹ $1200$
Second month rent off $=2 \times 1200=$ ₹ $2400$
So, rent after off $=12000-2400=$ ₹ $9600$ $\quad$ $\text {[for second month, total rent } =12000 \text { but after } 20 \% \text { off, rent } =9600]$
Now, at Savana apartment,
First month rent $=50 \%$ of 7000
$=\frac{50}{100} \times 7000$
$=$ ₹ $3500$
Second month rent $=$ ₹ $7000$
Total rent after off $=7000+3500$
$=$ ₹ $10500$
Difference between rents of the two apartments for the first two months $=10500-9600=$ ₹ $900$
So, Neelgiri apartments will be cheaper for the first two months by ₹ $900.$

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Question 35 Marks

In Dethi University, in the year $2009- 10,49000$ seats were available for admission to various courses at graduation level.
Out of these, 28200 seats were for the students of General category, while 7400 seats were reserved for SC and 3700 seats for ST.
Find the percentage of seats availale for
(i) students of General category.
(ii) students of SC and ST categories taken together.

Answer

Given, total seats were available for admission = 49000
Seats for General category = 28200
Seats for SC category = 7400
Seats for ST category = 3700
(i) Percentage of General category seats
$=\frac{28200}{49000}\times100$
$=57.55\%$
So, the percentage of seats available for students of General category is $=57.55\%.$
(ii) Total students of SC and ST categories
$=7400+3700=1100$
$\therefore$ Percentage of SC and ST categories seats
$=\frac{11100}{49000}\times100=22.65\%$
So, the percentage of seats available for students of SC and ST categories taken together is $22.65\%.$

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Question 45 Marks

Rahim borrowed ₹ $1024000$ from a bank for 2 yr. If the bank charges interest of $2.5\%$ per annum, compounded annually. Then, what amount will be have to pay after the given time period. Also, find the interest paid by him.

Answer

Given, principal $(\text P)=$ ₹ $1024000$
$\therefore$ Rate of interest $\text R=2.5\%$ and time $\text {(n)} =2\text{ yr}$
$\therefore$ Amount $=P\left(1+\frac{R}{100}\right)^{2}$
$=1024000 \times\left(1+\frac{2.5}{100}\right)^2 $
$ =1024000 \times \frac{1025}{1000} \times \frac{1025}{1000} $
$=$ ₹ $1075840$
$\therefore$ Compound Interest $=$ Amount - Principal
$=$ ₹ $1075840~-$ ₹ $1024000=$ ₹ $51840$
So, amount he have to pay is ₹ 1075840 and compound interest paid is ₹ 51840.

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Question 55 Marks

In $2007-08,$ the number of students appeared for Class X examination was $105332$ and in $2008-09,$ the number was $116054.$ If $88151$ students pass the examination in $2007-08$ and $103804$ students in $2008-09.$ What is the increase or decrease in pass$\%$ in Class X result?

Answer

From the given information, we have

Years	Number of students
Years	Appeard	Passed
$2007-2008$	105332	88151
$2008-2009$	116054	103804

Passing percentage of students of the Class X
examination in year 2007- 08
$\begin{array}{l}=\frac{\text { Number of students passed }}{\text { Number of students appeared }} \times 100 \\ =\frac{88151}{105332} \times 100=83.69 \%\end{array}$
Passing percentage of students of the Class X
$\begin{aligned} \text {examination in year 2008-09 } & =\frac{103804}{116054} \times 100 \\ & =89.44 \%\end{aligned}$
It is clear that in year 2008-09, passing percentage is increased by $(89.44 \%-83.69 \%)$ i.e. $5.75 \%$.

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