Given:

Time to clean full garden = 6 hours

Concept:

The fraction of the garden cleaned is proportional to the time spent cleaning.

Solution:

⇒ Fraction of garden cleaned in 2.5 hours = 2.5/6 = 5/12

Therefore, the fraction of the garden that can be cleaned in 2 hours 30 minutes is 5/12.

Let a number be ‘x’,

72% of a number is 90,

⇒ x × 72/100 = 90

⇒ x = 125

∴ Number is 125.

Given:

The marked price of an item is Rs. 800.

The shopkeeper offers two discounts, one of 10% and another of 5% on the item.

Concept used:

Now, the selling price of the item = 800 - 800 × 14.5%

⇒ 800 - 116

⇒ Rs. 684

∴ The selling price of the item is Rs. 684.

Given:

Two numbers in the ratio = 4 : 5

Product of the two numbers = 8820

Calculation:

Let the two numbers be 4x and 5x respectively

According to question

⇒ (4x × 5x) = 8820

⇒ 20x² = 8820

⇒ x² = 8820/20

⇒ x² = 441

⇒ x = 21

Now,

First number is 4x = 4 × 21 = 84

Second number is 5x = 5 × 21 = 105

Sum of total of the two numbers = (84 + 105)

⇒ 189

∴ Sum of total of the sum is 189

Given:

% of students who were absent in the class = 15%

Number of present students = 51

Formula used:

The formula of percentage.

X% of Y = XY/100

Calculation:

Let total number of students = x

Number of absent students = 15x/100

⇒ 3x/20

So, number of present students = x - 3x/20

⇒ 17x/20

17x/20 = 51

⇒ x = 60

∴ The total number of students is 60

Given:

65 liters of a mixture has kerosene to petrol ratio = 3 ∶ 2.

This ratio needs to be made 4 ∶ 5 by adding petrol.

Concept:

The amount of kerosene remains constant; adjust the petrol quantity.

Solution:

The current amount of kerosene in the mixture is (3/5) × 65 = 39 litres.

To achieve kerosene to petrol ratio of 4 ∶ 5, petrol must be 39 × (5/4) = 48.75 litres.

The extra petrol required is 48.75 - 26 (existing petrol) = 22.75 litres.

Hence, 22.75 litres of petrol should be added to the given mixture.

Given:

Principal (P) = Rs. 16,000

Time (T) = 2 years

Difference between Compound Interest (CI) and Simple Interest (SI) = Rs. 160

Concept:

The difference between Compound Interest and Simple Interest for two years is given by the formula: CI - SI = P × (r/100)2 

Solution:

⇒ Substituting the given values into the formula, 160 = 16000 × (r/100)2

⇒ Solving for r, we get r = 10

Therefore, the per annum rate of interest is 10%.

Given:

The LCM and HCF of the two numbers are 60 and 5.

One of the numbers is divided by 2 and the quotient is 10.

Concept used:

HCF of two or more numbers is the greatest factor that divides the numbers.

LCM is the smallest common multiple of two or more numbers.

Calculation:

One of the numbers = 2 × 10 = 20

Let the other number be 5p.

According to the question,

LCM (20, 5p) = 60

⇒ 5 × 4 × p = 60

⇒ p = 60/20

⇒ p = 3

Now, the other number = 5 × 3 = 15

∴ The other number is 15.

Given:

Diagonal of cube = 6√3 cm

Concept:

Diagonal = √3 × a

The volume of a cube =  a³

Calculation:

Side of the cube = Diagonal/√3 = 6√3 cm / √3 = 6 cm

Volume of the cube = (Side)³ = (6 cm)³ = 216 cm³

Therefore, the volume of the cube is 216 cm³.

Anit’s time when he starts his journey = Praneet’s starting time + 0:58:40

⇒ Anit’s time = 2:45:46 + 0:58:40 = 3:44:26 pm

Anit’s reaching time = Praneet’ reaching time + 0:50:29

⇒ Anit’s reaching time = 4:55:57 + 0:50:29 = 5:46:26 pm

∴ Time taken by Anit in journey = 5:46:26 – 3:44:26= 2:02:00 hrs= 2 hours 2 mins