Let cost price per cm = Rs 1,

Hence, cost price of 90cm = Rs 90

And, cost price of 100cm = Rs 100

Selling price of 100cm = 100 + 10% = Rs 110

∴ Actual profit percent = {(110 – 90)/90} × 100%

= (2/9) × 100% = 22.22%

Hence, the actual profit percent gained by the shopkeeper is 22.22%.

Given:

Average of 7 consecutive even number is 36.

Concept Used:

Average = Sum of number / Total Number

Calculation:

Let the 7 consecutive even numbers be x, x + 2, x + 4, x + 6, x + 8, x + 10, x + 12

⇒ Sum of 7 consecutive even numbers = 36 × 7 = 252

⇒ x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x + 12 = 252

⇒ 7x + 42 = 252

⇒ 7(x + 6) = 252

⇒ x + 6 = 36

⇒ x = 30

∴ lowest number x = 30

and highest number x + 12 = 42

∴ The difference between highest and lowest number = 42 - 30 = 12.

Given:

Difference between wages of A and C = Rs. 7600

Formula Used:

Share in wages = Work done/Total work × Total wages

Calculation:

Let total work be 60 unit,

Work done by A and B = 13/15 × 60 = 52 unit

⇒ Work done by C = 60 – 52 = 8 unit

Work done by B and C = 11/20 × 60 = 33 unit

⇒ Work done by A = 60 – 33 = 27 unit

Work done by B = 60 – 27 – 8 = 25 unit

According to the question,

27 – 8 = 19 unit = 7600

⇒ 1 unit = 400

Total wages of A and C = (27 + 8) = 35 units = 35 × 400 = Rs. 14000

Given:

Estimated profit = 5%

Reduction in profit = Rs.120

Percentage reduction in profit = 3.5%

Calculation:

By going through the ratio method,

⇒ CP    SP

20      21

200    210

Here, CP must be same

∴ CP    SP

⇒ 200  210

200  207

Change in profit = 10 - 7 = 3

⇒ 3 = 120

⇒ 1 = 40

CP will be 200 × 40 = 8000

∴ The correct answer is Rs.8000.

Given:

Principal = Rs. 24,000

Amount = Rs. 26,460

Rate of interest = 5% p.a.

Concept Used:

The formula for compound interest is: A = P (1 + r/n)^(nt), where n is the number of times interest is compounded per time period t.

Solution:

⇒ 26,460 = 24,000 (1 + 5/100)^(t)

⇒ (26,460/24,000) = (21/20)^(t)

⇒ t = log[(26,460/24,000)] / log[1.05] ≈ 2 years

⇒ In months, t = 2 x 12 = 24 months

Therefore, it will take 24 months for the sum to amount to Rs. 26,460.

Given:-

Radius of hemispherical solid = 14 cm

⇒ π = 22/7

Formula used:- 

Total surface area = 2πr² + πr² = 3πr²

Calculation:-

Total surface area = 3 × (22/7) × 14²

Total surface area = 3 × 22 × 14 × 2

Total surface area = 1848 cm²

Additional Information

Concept used:

If f(-a) = 0, then (x + a) is a factor of the polynomial f(x)

Calculation:

F(x) = (x – 2)(x² + Px + 4)

If (x – 3) is factor of f(x) then put x = 3 in equation (i) –

F(x) = 0

⇒ 0 = (3 – 2)(9 + 3P + 4)

⇒ (13 + 3P) = 0

⇒ P = -13/3

Let Peter and Preeti's age be A and B respectively.

The difference between Peter and Preeti’s ages is 5 years,

⇒ A – B = 5

35 years ago, 4 times Peter’s age was the same as 5 times the age of Preeti’s,

⇒ 4(A – 35) = 5(B – 35)

⇒ 4A – 140 = 5B – 175

⇒ 5B – 4A = 35

Solving,

⇒ 5B – 4(5 + B) = 35

⇒ 5B – 20 – 4B = 35

⇒ B = 55

⇒ A = 60

∴ Sum of their present ages = 60 + 55 = 115 years

Given:

Initial distance between thief and policeman = 500 m

Speed of thief = 8 km/h

Speed of policeman = 11 km/h

Concept used:

Relative speed and time = distance/speed

Solution:

Relative speed = speed of policeman - speed of thief = 11 km/h - 8 km/h = 3 km/h = 3 ×  (1000/3600) m/s = 5/6 m/s

Time taken to catch the thief = initial distance / relative speed 

Time taken to catch the thief = 500 m / (5/6 m/s) = 600 seconds

Distance run by the thief before he was caught = Speed of thief ×  time = (8 ×  1000/3600) m/s ×  600 s = 1333.33 meters

Therefore, the distance run by the thief before he was caught is approximately 1333.33 meters.

Shortcut Trick

Here, the thief and the police is running for the same time. So, time = constant.

When time is constant Speed ∝ Distance

Distance between the thief and the police  = 3 unit = 500 km

⇒ 1 unit = 500/3 

⇒ 8 unit = (500 × 8)/3 = 1333.33 m

Therefore, the distance run by the thief before he was caught is approximately 1333.33 meters.