Given:

One round of a circular park having a radius of 21 m is the same as that of a square park. 

Concept used:

The circumference of a circle = 2πR (R being the Radius)

The perimeter of a square = 4 × side

Calculation:

One round of a circular park is the same as that of a square park means the perimeter of the square park and the circumference of the circular park is the same.

Circumference of the circular park = 2π × 21 = 132 m

Now, the length of the side of the square park = 132/4 = 33 m

∴ The length of the side of the square park is 33 m.

Let P = principle, N = time and R = rate percent per annum

Then,

Simple interest = (P × N × R)/100

Given,

P = 1800, R = 8% and N = 3

Simple interest =

= (1800 × 8 × 3)/100

= 432

∴ Simple interest is Rs.432 on a principal of Rs. 1800 at the rate of 8% per annum for 3 years.

Given:

Total student = 90

Average marks of girls = 62

Average marks of boys = 70

Formula used:

Average = Sum of Data/Number of data

Calculation:

Girls in the class =  60% of 90 = 54

Boys in the class = 90 - 54 = 36

Average of all student = [54 × 62 + 36 × 70]/90

=(3348+2520)/90

⇒ 5868/90 = 65.2

∴ The average marks of all student is 65.2

Given:

Length of train = 130 m

Length of bridge = 110 m

Time taken to cross to bridge = 7.5 seconds

Concept:

The length calculated to cross the bridge is the length of the train and the bridge added together.

Formula used:

Speed = Distance/Time

Conversion from m/s to km/h = Multiply with 18/5

Calculation:

The total distance travelled by the train = 130 m + 110 m

⇒ 240 m

Speed of the train while crossing the bridge = 240/7.5 m/s

⇒ 32 m/s

Speed of the train in km/h = {32 × (18/5)} km/h

⇒ 115.2 km/h

∴ The speed of the train is 115.2 km/h.

Given:

The highest four-digit number which when divided by 3, 7, and 21 leaves the remainder 2.

Concept used:

Concept of LCM

Calculation:

According to the questions,

The highest four-digit number = 9999

L. C. M of  3, 7, and 21 = 21

⇒ 9999 ÷  21 

Remainder = 3

Now, 

Divisible number = 9999 – 3 = 9996

The required number that will leave the remainder 2

⇒ 9996 + 2 = 9998

∴ The highest four-digit number is 9998.

Given:

The price of pens was reduced by 30% due to which students bought 5 more pens.

Total money spent on purchasing pens = Rs. 140

Concept used:

Total expenditure = Price × Quantity

Calculation:

Let the price of one pen be Rs. x and the number of pens purchased be Rs. y.

Original expenditure = Price × Quantity

⇒ x × y = Rs. 140

Reduced price/new price of pen = x – 30% of x

⇒ 70% of x

⇒ 0.70x

New expenditure = 0.70x × (y + 5)

⇒ 0.70xy + 3.5x = Rs. 140

⇒ 0.70 × 140 + 3.5x = Rs. 140

⇒ 98 + 3.5x = Rs. 140

⇒ 3.5x = 42

⇒ x = Rs. 12

Reduced rate of pen = 0.70x

= 0.70 × Rs. (12)

⇒ Rs. 8.4

∴ The reduced price of the pen is Rs. 8.4.

GIVEN:

Successive discounts = 20% , 10% and 5% 

FORMULA USED:

Successive discount = X + Y - (XY)/100

Where,

X = First discount

Y = Second discount.

CALCULATION:

Let us take first two discounts i.e. X = 20%, Y = 10%.

⇒ Successive  discount

⇒ X + Y - (X Y)/100

⇒ 20 + 10 - (20 × 10 )/100 = (30 - 2) = 28%.

Now, Again X = 28% , Y = 5% 

Successive discount

⇒ X + Y - (X × Y)/100 

⇒ 28 + 5 - (140/100) = (33 - 1.4) = 31.6%.

Hence, one single equivalent discount is 31.60%.

Shortcut Trick

Let MP be 100

SP after discount = 100 × 80% × 90% × 95%

⇒ 68.4.

Hence, Discount = 100 - 68.4 = 31.6

∴ Discount% = 31.6%

Given:

40% of a number is less than its 60% by 30.

Formula:

x% of a number = Actual number × (x/100)

Calculation:

Let a number be x, then

According to the question

x × (60/100) - x × (40/100) = 30

⇒ x × (20/100) = 30

⇒ x = 30 × 5

⇒ x = 150

Hence, 20% of 150

⇒ 150 × (20/100)

⇒ 30

Shortcut Trick

60% of a number - 40% of a number = 30

⇒ 20% of that number = 30

Concept Used:

Calculation:

⇒ 20 - 2[25% of (15 × 8 ÷ 6 + 12)]

⇒ 20 - 2[25% of (15 ×4/3 + 12)]

⇒ 20 - 2[25% of (5 × 4 +12)]

⇒ 20 - 2[25% of (20 + 12)]

⇒ 20 - 2[25% of 32]

⇒ 20 - 16

∴ 4

Given:

Profit = 12%

Discount = 20%

Marked Price = ₹280

Formula Used:

MP/CP = (100 + Profit%)/(100 - Discount%)

Calculations:

MP/CP = (100 + Profit%)/(100 - Discount%)

⇒ 280/CP = (100 + 12)/(100 - 20)

⇒ 280/CP = (112)/(80)

⇒ 280/CP = 7/5

⇒ CP = 5/7 × 280

⇒ CP = ₹200

∴ The answer is ₹200.

Shortcut Trick

Discount % = 20% = 1/5

Ratio of M.P. to S.P. = 5 : 4  }_×7

Profit % = 12% = 3/25

Ratio of C.P. to S.P. = 25 : 28

So, combined ratio of C.P: S.P : M.P. = 25 : 28 : 35

⇒ 35 units = Rs. 280

⇒ 25 units = (280/35) × 25 = Rs. 200