Let the total number of votes polled be n

Given, one candidate got 40% of votes,

⇒ Number of votes received by loser = 40% of n = 40n/100

⇒ Votes % got by winner = 100 – 40 = 60%

So, Number of votes by winner = 60n/100

According to the question,

⇒ (60n/100) – (40n/100) = 298

⇒ 20n/100 = 298

⇒ n/5 = 298

⇒ n = 298 × 5 = 1490

∴ Total number of votes polled is 1490.

Given:

Total time is taken whole journey = 10 hrs.

The speed at whole journey = 48 km per hr.

Formula Used:

Distance = Speed × Times 

Distance = 48 × 10 = 480 kms

Now, this distance of 480 km is to be covered in 8 hours. Hence, the required speed

⇒ 480/8 = 60 km pe hr

Increased speed = 60 - 48 = 12 km/h

∴ The speed of the car must be increased by 12 km/h

Given:

A sum of money is divided among A, B, C and D in the proportion of 

B gets Rs. 70 more than A

Calculation:

Let the total sum be x

The ratio of all the sum is 

According to the qustion,

B gets Rs. 70 more than A

⇒ 4x/5 - 3x/4 = 70 

⇒ x/20 = 70 

⇒ x = 1400 

The share of D = (7/8)× 1400 

⇒ Rs. 1225

∴ The share of D is Rs. 1225.

Given:

If a sum doubles itself in 5 years by simple interest.

Time (T) = 5 years

Formula used:

S.I. = (P × R × T)/100

Where,

S.I. → Simple Interest

P → Principal

R → Rate 

T → Time

Calculations:

Let P be the principal amount and R be the rate of interest.

According to the question,

2P = P + (P × R × T)/100

⇒ P = (P × R × 5)/100

⇒ 1 = (R × 5)/100

⇒ R = 20%

∴ The rate of simple interest p.a. is 20%.

Given:

The ratio of the number of the students = 2 : 3 : 3

Number of students decreased by 60%, 30%, and 20%.

Calculation:

Let the number of students be 2X, 3X, and 3X.

According to the question,

Then, decreased students = 2X × 40%, 3X × 70%, 3X × 80%

The ratio of new number of students = 2X × 40% : 3X × 70% : 3X × 80%

⇒ Ratio = 80 : 210 : 240

⇒ Ratio = 8 : 21 : 24

∴ The new ratio of the number of students is 8 : 21 : 24.

Given:

Total cost of fencing = Rs. 10080

Cost of fencing per metre = Rs. 20

Concept used:

Perimeter = Total cost / Cost per metre

Area of the pavement = area of outer square - area of inner square.

Calculation:

According to the question,

Total cost of fencing = 10080

Perimeter of square = 10080/20 = 504 m

⇒ Side of square = 504/4 = 126 m

According to the diagram,

Breadth of the pavement = 2 × 3m = 6m

Side of inner square = 126 - 6 = 120m

Area of pavement = (126 × 126) - (120 × 120)

⇒ Area of pavement = 1476

Cost of pavement = 1476 × 50 = Rs. 73800.

∴ The cost of pavement is Rs. 73800.

Given:

A sells an article to B at a 20% profit.

B sells the article to C at a 10% profit.

C sells to D at a Rs. 16 profit.

The difference between D's price and A's cost is Rs. 500.

Concept used:

The concept of profit = selling price - cost price.

Calculation:

Let’s consider the cost of the article for A as Rs. X.

⇒ A sells the article at a 20% profit

⇒ So, B’s cost = Rs. 1.20X

⇒  B sells the article to C at a 10% profit

⇒ So, C’s cost = Rs. 1.1 × 1.20X = 1.32X

⇒ The selling price for D = C’s cost + profit

⇒  Rs. (1.32X + 16)

According to the question,

D's price - A's cost = Rs. 500,

⇒ 1.32X + 16 - X = 500

⇒ 0.32X = 484

⇒ X = Rs. 1512.5

Amount B paid to A to buy the article is 1.20 × 1512.5 = Rs. 1815.

∴ B paid Rs. 1815 to A to buy the article.

Shortcut Trick

Let, CP of A = 100a

CP for B = 100a × 120/100 = 120a

CP for C = 120a × 110/100 = 132a

CP for D = 132a + 16

According to the question,

132a + 16 - 100a = 500

⇒ a = 484/32 = 121/8

CP for B = 120 × 121/8 = Rs. 1815

Given:

Two pipes P and Q can fill a tank in 25 minutes and 30 minutes, respectively.

Both the pipes are opened together, but after 5 minutes pipe P is turned off.

Formula used:

Total capacity of tank = Efficiency of the pipe ×  Operational time of the pipe 

Calculation:

Let the total capacity of tank = 1 unit

The time taken by P to fill the tank = 25 min

⇒ t = 24 min

Therefore, "24 min" is the required answer.

Given:

Total students = 15

Average age of students = 18 - 1 = 17 years

Average age of students and teachers = 18 years

Concept used:

Average = Sum of observation / Number of observations

Calculation:

Let, the age of the teacher = m

Sum of ages of 15 students = 15 × 17 = 255

⇒ 255 + m = 288

⇒ m = 288 - 255 = 33

∴​ The age of the teacher is 33 years.

Given:

The ratio of a fruit costing Rs. 20 per kg and Rs. 38 per kg = 5 : 4.

The cost of fruits = Rs. 20 per kg

The cost of fruits= Rs. 38 per kg

Formula used:

Total value = Quantity × price

Solution:

Let the two types of oil be 5x and 4x.

Total cost of the mixture = (5x × 20) + (4x × 38)

⇒ 100x + 152x = 252x

The cost per kg of the resulting mixture:

⇒ 252x/9x

⇒ 28

The answer is Rs. 28 per kg.