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Given:

Principal = Rs. 6000 

Amount = Rs. 8340 

Rate = 13% 

Time = K

Formula used:

S.I = PRT/100

Where P → principal, R → rate, T → time 

Simple interest = Amount - Principal

Calculation:

According to the question,

Simple interest = 8340 - 6000 = 2340 

By using formula, we get 

Simple interest = (6000 × 13 × K)100

⇒ 2340 = 780 × K 

⇒ 3 = K 

∴ The value of K is 3 years.

Given:

Total number of movies = 200

W4 = 20% of total movies 

W1 = 12% of total movies

Calculation:

According to the question,

100% → 200 movies

⇒ 1% → 2 movies 

Number of movies released in W4 = 20%

⇒ 20 × 2 = 40

Number of movies released in W1 = 12%

⇒ 12 × 2 = 24

Required difference = 40 - 24

⇒ 16

∴ In week 'W4' 16 more movies released as compared to 'W1'.

Given:

Total distance =  250 km

Total time = 30 h

Car covered 1/5 part of the journey in 1/6 time.

Formula Used:

Speed = Distance/Time

Calculation:

According to the question,

Distance travelled by car = (1/5) × 250

⇒ 50 km

Time taken to travel this distance = (1/6) × 30

⇒ 5 hours

So, Remaining distance to be travelled by car = 250 - 50

⇒ 200 km

&, Remaining time to travel this distance = 30 - 5

⇒ 25 hours

Now, Speed of the car for the remaining journey = (Remaining distance)/(Remaining time)

⇒ 200/25

⇒ 8 km/hr

∴ The speed of the car to cover the remaining journey on time is 8 km/hr.

Given:

Two cubes combined to form a single cuboid

Edge of cube = 24 cm

Formula used:

Volume of a cuboid = L × B × H,

where,

L = Length, B = Breadth, H = Height of the cuboid

Calculation:

According to the question,

Two cubes each of edge 24 cm are combined to form a single cuboid.

Observe the following diagram for better understanding.

So, After combining the cubes,

Length of the cuboid = 24 + 24 

⇒ 48 cm

Breadth of the cuboid = 24 cm

& Height of the cuboid = 24 cm

So, Volume of the cuboid = L × B × H

⇒ 48 × 24 × 24 

⇒ 27648 cm³

∴ The volume of the new cuboid is 27648 cm3.

Given:

Rotis made on D5 = 1296

Rotis made on D1 = 1024

Calculation:

According to the question,

Required percentage = [(Rotis made on D5 - Rotis made on D1)/(Rotis made on D1)] × 100%

⇒ [(1296 - 1024)/1024] × 100%

⇒ (272/1024) × 100%

⇒ (17/64) × 100%

⇒ 26.56%

∴ The rotis made on D5 is 26.56% percent more than the rotis made on D1.

Given:

Amount in 3 years = Rs. 39930

Amount in 2 years = Rs. 36300

Formula used:

A = P(1 + r/100)ⁿ

Where, A = Amount, r = Rate of interest, n = Time in year

Calculation:

According to the question,

39930 = P(1 + r/100)³      ----(1)

36300 = P(1 + r/100)²      ----(2)

Dividing equation (1) by equation (2), we get

(39930/36300) = [(1 + r/100)³/(1 + r/100)²]

⇒ 11/10 = 1 + r/100

⇒ r/100 = 1/10

⇒ r = 10%

From equation (2),

36300 = P[1 + (10/100)]²

⇒ 36300 = P(11/10)²

⇒ P = 36300 × (100/121)

⇒ P = 30000

∴ The sum is Rs. 30000.

Shortcut Trick

Percentage increase = 36300 - 39930 = 3630

⇒ (3630 / 36300) × 100 = 10%

let the principal be x

⇒ x + (10/100)² × x = 36300

⇒ 1.21x = 36300

⇒ x = 36300 / 1.21 = Rs.30000

 ∴ The sum is Rs. 30000.

Given:

A completes the work = 8 days

B completes the work = 12  days

C completes the work = 16 days

Total wages = Rs. 12000

Concept used:

The total work will be LCM of individual time taken by A and B and C. 

Efficiency α Share

Calculation:

Total work = LCM of (8, 12, 16)

⇒ Total work = 48

Efficiency of A = 48/8 = 6

Efficiency of B = 48/12 = 4

Efficiency of C = 48/16 = 3

⇒ The total efficiency of A , B and C = 13

Total efficiency of A, B, C and D = (48/3) = 16

Efficiency of D = 16 - 13

⇒ The efficiency of D = 3

The share will be distributed in the ratio of 6 ∶ 4 ∶ 3 ∶ 3.

Let the share of A, B, C and D be 6x, 4x, 3x and 3x

According to the question, 

Total share = Rs. 12000

⇒ 6x + 4x + 3x + 3x = 12000

⇒ x = 12000/16

⇒ x = 750

Share of D = 3 × 750

⇒ Share of D = Rs. 2250. ∴ The share of D is Rs. 2250.

Given:

The number of questions in set 1 = 54

The number of questions in set 4 = 62

Calculation:

Let the number of questions in set 1 be x less than the number of questions in set 4.

According to the question, 

x = 62 - 54

⇒ 8

Now, Required percentage = (8/62) × 100%

⇒ (400/31)%

⇒ 12.903%

∴ The number of questions in set 1 is approximately 12.9% less than the number of questions in set 4.

Given:

Number of days taken by 100 men to make 60 chairs working 2 hours a day = 4 days

Chairs to be made in 10 days working 4 hours a day = 120

Formula used:

(M1 × D1 × H1)/W1 = (M2 × D2 × H2)/W2

Where, M1, M2 = Number of men D1, D2 = Number of days, H1, H2 = Number of hours, W1, W2 = Work Done

We will use only the terms that are given in the question

Calculation:

According to the question,

M1 = 100, D1 = 4 days, H1 = 2 hours and W1 = 60 chairs

D2 = 10 days, H2 = 4 hours and W2 = 120 chairs

(M1 × D1 × H1)/W1 = (M2 × D2 × H2)/W2         

⇒ (100 × 4 × 2)/60 = (M2 × 10 × 4)/120

⇒ 100 × 8 × 120 = M2 × 40 × 60

⇒ M2 = 40

∴ 40 men are required to make 120 chairs in 10 days working 4 hours a day.

Given:

The length of the cuboid = 12 cm

The breadth of the cuboid = 9 cm

The height of the cuboid = 8 cm

Formula used:

D = √(l² + b² + h²)

where, D = The longest diagonal of a cuboid, l = The length of a cuboid

b = The breadth of a cuboid, h = The height of a cuboid

Calculation:

According to the question, 

D = √(122 + 92 + 82)

⇒ √(144 + 81 + 64)

⇒ √289

⇒ 17 cm

∴ The longest diagonal of the cuboid is 17 cm.