Given:

Increment in number = 10% of the number

Decrement in number = 20% of the new number

Concept used:

Net increase or decrease percent = {(Original number or Final number) - (Final number or original number) ÷ Original number} × 100

Calculation:

Let the original number be 100

When the number is increased by 10%

New Number = 100 + 10% of 100

⇒ 100 + 10

⇒ 110

Now, the number is decreased by 20%

Final number = New number – 20% of new number

⇒ 110 – 20% of 110

⇒ 110 – 22

⇒ 88

∴ Net Decrease in percentage = { (100 – 88) / 100} × 100

⇒ {12/100} × 100

⇒ 12%

∴ The net decrease percentage is 12%.

Shortcut Trick

Formula used: (It is only valid for this type of question)

Where,

+x% is the percentage increased in price

-x% is the percentage decreased in price

+y% is the percentage increased in consumption

-y% is the percentage decreased in consumption 

According to the question,

The percentage increase in price is 25%

The percentage decreased in consumption is x%

Therefore,

Therefore, the consumption of petrol is decreased by 25%.

The required answer is 25%.

Alternate Method

Given: 

The ratio of new expenditure to that of the initial expenditure is 15 : 16. 

If the price of petrol is increased by 25% then the consumption of petrol is decreased by x%.

Concept used:

Expenditure = Price × Consumption

Calculation:

Let the initial price of petrol = ₹100

Let the initial consumption of petrol = 100 L

Therefore, 

The initial expenditure = ₹100 × 100 = ₹10,000

In the second case:

The increased price of the petrol = (100% + 25%) of ₹100 = ₹125

The decreased consumption of the petrol = (100% - x%) of 100 L

The new expenditure = ₹125 × (100% - x%) of 100 L

According to the question,

⇒ 3 = 4(1 - x%)

⇒ 4x% = 1

⇒ x = 25%

Therefore, the consumption of petrol is decreased by 25%.

∴ The required answer is 25%.

Given:

C.P = Rs. 5400

C.P = Cost Price

Calculation:

According to the question,

⇒ (3600 × 8%) + (1800 × x%) = (5400 × 18%)

⇒ 288 + 18x = 54 × 18

⇒ 288 + 18x = 972

⇒ 18x = 972 - 288

⇒ x = 684/18

⇒ x = 38

∴ The correct answer is 38%.

Given:

Number = 27B58A4

The number is divisible by 88

Concept Used:

The divisibility rule of 8 is the last 3-digit number must divisible by 8

The divisibility rule of 11 is the difference between a sum of alternative numbers that must be divisible by 11 or can be 0.

Calculations:

According to the question,

⇒ Number = 27B58A4

⇒ last 3-digit number = 8A4

⇒ when we put A = 2

⇒ then the last 3-digit becomes = 824, which is divisible by 8

⇒ and when we put A = 6

⇒ then the last 3-digit becomes = 864, which is also divisible by 8

But the least number is 2

⇒ So, The value of A = 2

⇒ Now, The number becomes = 27B5824

⇒ Sum of numbers in even place = 7 + 5 + 2 = 14

⇒ Sum of numbers in odd places = 2 + B + 8 + 4 = 14 + B

⇒ Difference = 14 + B - 14 = B

here B must be divisible by 11

⇒ so, 0 is the only number that can divisible by 11

⇒ So, the Value of B = 0

⇒ now, Value of A + B = 2 + 0 = 2

⇒ Thus, The least value of A + B is 2.

Hence, the correct answer is option 2).

Given:

Product of digits = 12      ---- (1)

Calculation:

Let the number be ab.

According to question

(10a + b) + 36 = 10b + a

⇒ 9b - 9a = 36

⇒ b - a = 4      ---- (1)

Squaring both sides, we get

b² + a² - 2ab = 16

⇒ b² + a² - 2ab + 4ab = 16 + 4ab

⇒ (b + a)² = 16 + 4 × 12

⇒ (b + a)² = 64

⇒ b + a = 8 ---- (2)

Adding (1) and (2), we get

2b = 12

⇒ b = 6

Now, a = 8 - b = 8 - 6 = 2

∴ Required number = 26

Shortcut Trick

By option method

As we know that in question it is given that product of digit of number = 12 

According to this given part all option are correct

Now go with other given part

(I) - 34

34 + 36 = 70 not equal to 43 (reverse digit)

(ii) 43

43 + 36 = 79 not equal to 34 (reverse digit)

(iii) 62

62 + 36 = 98 not equal to 26 (reverse digit)

(iv) 26

26 + 36 = 62 = 26 (reverse digit)

Shortcut Trick

Alternate Method

Given:

The two road is at right angle 

Speed of bus A = 48 km/h

Speed of bus B = 36 km/h

Formula Used:

Speed = Distance / Time

By Pythagoras theorem

Hypotenuse² = Base² + Height²

Calculations:

⇒ Speed of Bus A = 48 km/h = 40/3 m/s

⇒ Speed of bus B = 36 km/h = 10 m/s

Bus A travel distance in 15 sec

⇒ Distance = 40/3 x 15 = 200 m

Bus B travel distance in 15 sec

⇒ Distance = 10 x 15 = 150 m

as the two road is at right angle, so

⇒ Let Height = 200 m

⇒ Base = 150 m

By Pythagoras theorem

Hypotenuse2 = Base2 + Height²

⇒ Distance between two buses = 200² + 150² = 40000 + 22500 = 62500 = 250 m

⇒ Hence, Distance between the two buses is 250 m

Multiply 72 in equation (1)

A : B : C = 12 : 9 : 8

According to question,

A + B + C = Rs. 3596

⇒ 12x + 9x + 8x = Rs. 3596

⇒ 29x = Rs. 3596

x = 124

Then, A = 1488, B = 1116, C = 992

Now, The difference (in ₹) between the shares of A and C

A - C = 1488 - 992 = 496

∴ The difference (in ₹) between the shares of A and C = Rs. 496

Given:

Speed of train =  72 km/h

Length of train = 240

Crosses a platform in 40 seconds

Formula used:

Speed x Time = Distance

Calculation:

Speed = 72 x 5/18 = 20m /sec

Speed x Time = Distance

⇒ 20 x 40 = 240 +x

⇒ 800 = 240 + x

⇒ x = 560 m

hence, option 2 is correct answer.

Given:

Profit (P) = 10%

Increase in price = 20%

Discount (D) = 10%

Dishonesty = 10%

Formula used:

S.P = M.P - D

S.P = Selling Price

M.P = Marked Price

Effective Profit = x + y + (x × y)/100

{(S × De)/R - 100}

S = Situation of Shopkeeper

De = Demand of Quantity by Customer

R = Received Quantity to Customer

Calculation:

Let the Cost price (C.P) by 100

⇒ C.P = 100

Increased price = 120

⇒ S.P = 120 - 12 

⇒ S.P = 108

Effective Profit = x + y + (x × y)/100

⇒ 10 + 8 + (10 × 8)/100

⇒ 18.8

The situation of shopkeepers is 18.8 profit 

⇒ {(S × De)/R - 100}

⇒ {(108.8 × 100)/90 - 100}

⇒ 132 - 100

⇒ 32

∴ The net gain is 32%.

Shortcut Trick

Calculation:

We can use successive method.

C.P : S.P = 4500 : 5940 = 25 : 33

Profit% = {(33 - 25)/25} × 100 = 32%

∴ The correct answer is 32%.

Given:

In an election, the candidate who secured 64% of the votes polled, won by 504 votes.

90% voters cast their vote.

Calculations:

Let the number of voters on the voting list be x.

The candidate winning be = 64% of x.

The candidate loosing be = (100 - 64)% = 36% of x.

Now, 64% of x - 36% of x = 504

0.64x - 0.36x = 504