Explanation

Initially, the total height of the 14 boys = Average height x Number of boys = 5.3 x 14 = 74.2 feet

After the new boy joined, the total height of the 15 boys = New average height x Total number of boys = 5.25 x 15 = 78.75 feet

Since the total height increased by the height of the new boy, we can set up the equation:

74.2 + New boy's height = 78.75

Subtract 74.2 from both sides:

New boy's height = 78.75 - 74.2

New boy's height = 4.55 feet

So, the new boy's height is 4.55 feet.

Explanation

Let the five consecutive even numbers be 2(x – 2), 2(x – 1), 2x, 2(x + 1) and 2(x + 2)

Their sum = 10x = 440

x = 44 => 2(x – 2) = 84

Second least number of the other set = 2(84) – 121 = 47

This set has its least number as 46.

Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50

= 48 – 2 + 48 – 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240

Explanation

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius.

Given the area is 98.56 cm^2, we can set up the equation:

98.56 = πr^2

Now, divide both sides by π (approximately 3.14):

r^2 = 98.56 / 3.14

r^2 = 31.36

r = √31.36

r ≈ 5.6

Now that we have the radius, we can find the circumference using the formula:

C = 2πr

C ≈ 2 × 3.14 × 5.6

C ≈ 35.2

So, the circumference is approximately 35.2 cm.

Explanation

Principal amount (P) = Rs. 12,500

Amount after 4 years (A) = Rs. 15,500

Time (T) = 4 years

Interest (I) = A - P = Rs. 15,500 - Rs. 12,500 = Rs. 3,000

Rate of interest (R) = (I / P) × (1 / T) × 100%

= (3,000 / 12,500) × (1 / 4) × 100%

= 6%

Explanation

Quantity of milk  =(60×32​) litres =40 litres

Quantity of water in it =(60−40) litres =20 litres

New ratio =1:2

Let the quantity of water to be added further be x litres

Then milk : water  =(20+x40​)

Now, (20+x40​)=21​

=> 20+x=80

=> x=60

Explanation

Systematic risk refers to the risk inherent to the entire market or market segment.

Market risk is also known as systematic risk.