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Given:

Total principal = Rs. 20,000

Rate = 8% and 15%

Time = 3 years

S.I = Rs. 6480

Formula Used:

S.I = PRT/100

Where,

S.I = Simple interest, P = Principal,

R = Rate of interest, T = Time duration

Calculation:

Let the principal at the rate of 8% and 15% be x and (20000 - x) respectively

According to the question, we have

(x × 8 × 3)/100 + {(20000 - x) × 15 × 3}/100 = 6480

⇒ 24x + 900000 - 45x = 648000

⇒ 45x - 24x = 900000 - 648000

⇒ 21x = 252000

⇒ x = 12000

and,

(20000 - x) = (20000 - 12000)

⇒ 8000

∴ The value of the first and second part is Rs. 12000 and Rs. 8000.

Alternate Method

Total interest = Rs. 6480

Total interest rate = (6480/20000) × 100 = 32.4

Interest per annum = 32.4/3 = 10.8%

Part invested at 8% interest = [3/(3 + 2)] × 20,000 = 12,000

Part invested at 15% = 20,000 - 12,000 = 8,000

∴ The value of the first and second part is Rs. 12000 and Rs. 8000.

Given:

The ratio of salaries of P, Q and R = 3 ∶ 5 ∶ 8

The salaries increment in P, Q and R = 20%, 20% and 5%

Calculation:

According to the question, we have

P ∶ Q ∶ R = 3 ∶ 5 ∶ 8

⇒ Let P ∶ Q ∶ R be 300 ∶ 500 ∶ 800

Now, the salaries increased by 20%, 20% and 5%

P ∶ Q ∶ R = 300(120/100) ∶ 500(120/100) ∶ 800(105/100)

⇒ P ∶ Q ∶ R = 360 ∶ 600 ∶ 840

⇒ P ∶ Q ∶ R = 3 ∶ 5 ∶ 7

∴ The ratio of increased salaries of P, Q and R are 3 ∶ 5 ∶ 7.

Given:

C7 female employees = 108

C5 female employees = 92

Calculation:

No. of female employees more than in C7 to C5 = 108 - 92 = 16

Required percentage = (16/92) × 100 = 17.39

∴ Required percentage is 17.39%.

Given:

(The efficiency of Vikram)/(The efficiency of Kushal) = 300/100 = 3/1

Number of hours required to complete a piece of work by Vikram = 100 hours

Formula used:

Total work = (Efficiency) × (Number of days required to complete the work)

Calculation:

Sum of efficiency of Vikram and Kushal = 4

The efficiency of Vikram = 3

Total work = 3 × 100 = 300

Number of hours to complete the whole work done by Vikram and Kushal = 300/4

⇒ 75 hours

∴ 75 hours to complete the whole work done by Vikram and Kushal.

Given:

Percentage of T1 = 12%

Percentage of T3 = 28%

Formula Used:

Central angle of sector = (Given % of sector/100) × 360° 

Calculation:

Difference between sector T1 and T3 = 28% - 12% = 16%

100% = 360°

⇒ 1% = 360°/100

⇒ 16% = (360°/100) × 16 

⇒ 57.6°

∴ The difference between central angle of sector T1 and T3 is 57.6°.

Given:

Speed of a boat in still water = 18 km/hr

Speed of stream = 4 km/hr

Distance = 44 km

Formula used:

Speed of downstream = (u + v)

Time = Distance/Speed

Where u = The speed of a boat still water,

v = The speed of the stream 

Calculation:

Speed of downstream = (u + v)

⇒ Speed of downstream = (18 + 4) = 22 km/hr

Time taken to travel 44 km downstream = Distance/Speed

⇒ 44/22

⇒ 2 hours

∴ Time taken to travel 44 km downstream is 2 hours.

Formula used:

Average = Sum of the marks/Numbers of Subject

Calculation:

Average marks = Sum of the marks/Numbers of Subject

⇒ Average marks = (80 + 90 + 70 + 84 + 86 + 92 + 88 + 81 + 99 + 97)/10

⇒ Average marks = 867/10 = 86.7

∴ The average marks obtained by students per subject is 86.7

Given:

Area of the passage = 128 m²

Width of passage = 4 m

Formula used:

Area of square = a²

Where, a = Side of the square

Calculation:

Area of the Room = a²      ----(1)

Area of the room with passage = (a + 8)²      ----(2)

Area of the passage = Area of the room with passage - Area of the room 

⇒ 128 = (a + 8)² - a²

⇒ 128 = (a + 8 + a ) × (a + 8 - a)

⇒ 128 = (2a + 8) × 8

⇒ 16 = 2a + 8

⇒ a = 4

From equation (1)

Area of the room = a²

⇒ (4)²

⇒ 16 m²

∴ The area of the square is 16 m².

Given:

Total amount = Rs. 420

Available coins are 5 rupees, 2 rupees, and 1 rupee.

The ratio of the coins = 2 ∶ 3 ∶ 5

Calculation:

Let the ratio of 5 rupees, 2 rupees and 1 rupee coins be 2x, 3x and 5x respectively.

⇒ The total coins = 2x + 3x + 5x

⇒ The total coins = 10x      ----(1)

Then the amount of 5 rupees, 2 rupees, and 1 rupee coins be 10x, 6x, and 5x respectively.

⇒ The total amount = 10x + 6x + 5x

⇒ The total amount = 21x

According to the question,

⇒ 21x = Rs. 420

⇒ x = Rs. 20

From equation (1)

The total coins = 10x

⇒ The total coins = 200

∴ The total number of coins in the bag is 200.

Given:

Speed of bus = 81 km/h

Distance = 9/2 km

Formula used:

S = D/T

Where, S = Speed, D = Distance, T = Time

Calculation:

S = D/T

⇒ 81 = (9/2)/(T)

⇒ T = (1/18) hour

⇒ T = (3600/18) second

⇒ T = 200 sec

∴ The bus will take 200 seconds to cover the distance.

Additional Information

 1 hour = 3600 seconds