# Area

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

Let C.P. of each article be Rs. 1  C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20 - x).

∴ $$\frac{20 - x}{x} \times 100 = 25$$

⇒ 2000 - 100x = 25x

⇒ 125= 2000

= 16

Jo’s collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?

Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.

US : Indian = 5 : 2, and

Indian : British = 5 : 1.

Multiply the first by 5, and the second by 2.

Hence the two ratios can be combined and

US : British = 25 : 2

Now,

US : Indian = 25 : 10, and

Indian : British = 10 : 2

A bag contains 50 P, 25 P and 10 P coins in the ratio 5 : 9 : 4, amounting to Rs. 206. Find the number of coins of each type respectively.

Let ratio be x.Hence no. of coins be 5x ,9x , 4x respectively.

Now given total amount
= Rs. 206 ⇒ (.50)(5x) + (.25)(9x) + (.10)(4x)

= 206 we get x = 40 ⇒ No. of 50p coins

= 200

⇒ No. of 25p coins = 360

⇒ No. of 10p coins = 160

Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits ?

The fruit content in both the fresh fruit and dry fruit is the same.

Given, fresh fruit has 68% water. so remaining 32% is fruit content. weight of fresh fruits is 100 kg.

Dry fruit has 20% water. so remaining 80% is fruit content.

Let weight if dry fruit be y kg.

fruit % in fresh fruit = fruit % in dryfruit

(32/100) × 100 = (80/100 ) × y

we get, y = 40 kg

The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field ?

Let breadth = x metres.
Then length =(115x/100) metres.

x × (115x/100) = 460

⇒ x2 = (460 × 100/115)

⇒ x2 = 400

⇒ x = 20

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

Let the side of the square(ABCD) be x meters.

Then, AB + BC = 2x metres.

AC =  √2x = (1.41x) m.

Saving on 2x metres = (0.59x) m.

Saving % = (0.59x/2x) × 100 % =30% (approx)

A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 75 paise per sq. m is

Area to be plastered
= [2 (l + b) × h] + (l × b)
= [2 (25 + 12) × 6] + (25 × 12)
= 744 sq. m

Cost of plastering = 744 × (75/100)
= Rs. 558

If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

Let original radius = R.

New radius =b(50/100) R = (R/2)

Original area ΠR2 and new area= $$\pi \left ( \frac{R}{2} \right )^{2} = \frac{\pi R^{2}}{4}$$

Decrease in area

= $$\frac{3\pi R^{2}}{4} \times \frac{1}{\pi R^{2}} \times 100$$

= 75%

If each side of a square is increased by 25%, find the percentage change in its area?

Let each side of the square be a,

then area = a × a

New side = 125a/100 = 5a/4

New area = (5a × 5a) / (4 × 4)

= (25a²/16)

increased area== (25a²/16) - a²

Increase % = [(9a²/16 ) × (1/a² ) × 100] %

= 56.25%

The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

Let $$\sqrt{l^{2} + b^{2}} = \sqrt{41}$$