Question

Q.30) If the circumference of a circle is 176cm find its radius.
2 Q.31) On selling a sofa set for Rs 21,600 a dealer gain 8% for how much did he purchase it.​

Answer 1

30)

Given :-

• Circumference = 176cm

To know :-

★ Circumference of Circle = 2πr

• Here , r is dadius of circle and π = 22/7.

Solution :-

We know ,

Circumference = 2 × π × r

Putting values ,

→ 176 = 2 × (22/7) × r

→ 176 = 44r/7

→ 176 × 7 = 44r

→ 1232 = 44r

→ r = 1232/44

→ r = 28cm

Hence , radius of circle is 28cm.

_________________________

31)

Given :-

• Dealer sells a sofa for Rs 21,600 gaining 8% profit.

To find :-

• Buying price of sofa.

Solution :-

Let the buying price of sofa be 'x'.

We know that the dealer gained 8% profit.

Selling price = Buying price + 8% of buying price

→ 21600 = x + 8% of x

→ 21600 = x + (8/100)x

→ 21600 = x + (8x/100)

→ 21600 = 108x/100

→ 2160000 = 108x

→ x = 2160000/108

→ x = 20,000 Rs

Hence , dealer bought the sofa at Rs20,000.

Answer 2

Question -

$\sf \: If \: the \: circumference \: of \: a \: circle \: is \\\sf \: 176cm \: find \: its \: radius. \:$

Answer -

Given :

• Circumference of a circle = 176cm

To find :

• Radius

Solution :

Circumference of a circle is 176cm

i.e 2πr = 176

$\;\;\bf{\;\;\blue{2 \times \frac{22}{7} \times r = 176 }}$

$\;\;\bf{\;\;\red{r = 28 \: cm}}$

$\;\;\bf{\;\;\green{Radius = 28 \: cm}}$

Question -

• On selling a sofa set for Rs 21,600 a dealer gain 8% for how much did he purchase it.

Answer -

Given -

• Selling a sofa set for Rs 21,600 a dealer gain 8% .

To find -

• How much did he purchase .

Solution -

Dealer Selling sofa for = Rs 21600

= Selling price

• He gain on selling = 8%

The cost price of sofa set is

CP = Rs {( 100/(100 + gain %)) × SP }

$={(100/(100+8))×21600}$

$={(100/108)×21600}$

$={2160000/108}$

$=Rs.20000$