Given:

Initial distance between cop and thief: 120 m

Speed of thief: 6 m/sec

Speed of cop: 8 m/sec

Concept used:

Relative speed is the difference of individual speeds, and the distance covered by the thief before the cop catches him is the product of the thief's speed and the time it takes for the cop to catch him.

Solution:

Calculate the relative speed: 8 m/sec - 6 m/sec.

Calculate the time for the cop to catch the thief: 120 m / relative speed.

Calculate the distance covered by the thief: thief's speed * time.

⇒ Relative speed = 8 m/sec - 6 m/sec = 2 m/sec

⇒ Time = 120 m / 2 m/sec = 60 sec

⇒ Distance covered by the thief = 6 m/sec × 60 sec = 360 m

Therefore, the thief covers a distance of 360 m before the cop catches him.

Given:

SI at 12% is Rs56 less than Amount at 9%

Formula Used:

A = P + PRT/100 = P(1 + RT/100)

SI = (P × R × T)/100

Calculation:

⇒  P × 21/2 × 12/100 = P(1 + 27/100) - 56

⇒ P × 126/100 = P × 127/100 - 56

⇒ 127P/100 - 126P/100 = 56

⇒ P/100 = 56

⇒ P = 5600

∴ The correct answer is Rs.5600.

Given:

A can paint 5 chairs in an hour

B can paint 3 chairs in an hour

Solution:

⇒ A and B together can paint (5+3) chairs in an hour = 8 chairs

⇒ Time required to paint 40 chairs = 40/8 = 5 hours

Hence, A and B will require 5 hours to paint 40 chairs together.

Given:

Diameter of sphere = 12 cm

Length of wire = 48 cm

Formula used:

Volume of sphere = (4 / 3)π × radius³

Volume of cylinder = π × radius² × height

Calculation:

According to question

Volume of cylinder (wire) = volume of sphere

⇒ π × radius² × 48 = (4 / 3) × π × 6 × 6 × 6

⇒ radius² = (4 × 6 × 6 × 6) / 3 × 48

⇒ radius² = 6

⇒ Radius = √6 cm

Diameter = 2 × radius

∴ Diameter of cylinder (wire) = 2√6 cm

Given:

Principal = Rs.60000 ; Rate% = 10% ; Time = 5 years

Formula used:

A = P × (100 + R%)^T

Compound interest (C.I) = (A - P)

Where, A = amount ; P = principal ; T = time ; R = rate

Calculation:

Amount = P × (100 + R%)T

⇒ 60000 × (110/100)⁵

⇒ 60000 × (11/10)5

⇒ 60000 × (161051/100000)

⇒ 6 × 16105.1 = 96630.6

Compound interest (C.I) = (A - P)

⇒ 96630.6 - 60000 = 36630.60

∴ The correct answer is Rs.36630.60.

The bar-graph shows the number of employees working in 5 different sectors

Given:

The ratio of number of male and female employees

Calculations:

The total number of employees is sector S = 800

The ratio ​The ratio of number of male and female employees in sector S = 3 : 5

The number of males from sector S = 3/(3 + 5) × 800

= 3/8 × 800

= 300

Hence, The number of males from sector S is "300"

Given:

A woman invests Rs. 100 at the start of each year

P = 100

Rate of Interest, R = 5% P.A

Number of years, N = 2

Formula used:

Amount, A = P[1 + (R/100)]^N

Calculation:

For the 1^st year,

N = 1

A = 100[1 + (5/100)]¹

A = 105

According to the question:

Invests Rs. 100 at the start of each year

For the 2^nd year,

P = 105 + 100 = 205

N = 1

⇒ A = 205[1 + (5/100)]¹

⇒ A = 215.25

∴ Her investment at the end of the 2nd year = Rs. 215.25

Given:

Numbers 6 and 110

Concept:

The least common multiple (LCM) of two integers a and b,

usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b.

Steps:

Prime factorization of 6 = 2 × 3

Prime factorization of 110 = 2 × 5 × 11

LCM = Product of highest powers of all factors

⇒ 2 × 3 × 5 × 11 = 330

Hence, the LCM of 6 and 110 is 330.

Given:

The Data of Union Territory Area's

Solution:

The Area of Delhi in percentage = 44%

And The Area of Chandigarh in Percentage = 4%

Difference between Area of Delhi and Chandigarh = (44 - 4) %

⇒ 40%

Percentage bigger than Delhi form Chandigarh = (40 / 4) × 100

⇒ 10 × 100 = 1000 %

Delhi is 1000 % more Bigger than Chandigarh.

Concept:

Ratio of all sides of two similar triangle is always equal.

Given:

ΔABC ~ Δ RST

∴ AB / RS = AC / RT = BC / ST

⇒ AB/6 = 1/4

⇒ AB = 1.5