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Invalid vote in block B are 

⇒ 300+400+200

⇒ 900

⇒ 900/3

⇒ 300

Hence 300 is the correct answer.

Invalid vote in Block A in 2015 is 1400 - 1200 = 200

Invalid vote in Block B in 2016 is 2200 - 1800 = 400

Ratio of these invalid votes in respective years = 200 : 400

⇒ 1 : 2

Hence 1 : 2 is the correct answer.

B invalid in 2015 is 1800 - 1500 = 300

A invalid in 2017 is 1200 - 950 = 250

⇒ (300 - 250 ) = 50

⇒ (50 / 250 )× 100

⇒ 20%

Hence 20% is the correct answer

1. Valid vote in block A is 

   ⇒ 1200+ 800 + 950

   ⇒ 2950/3 = 983.33

   Hence statement 1 is wrong 

2. invalid vote in Block A 2016 is 1000-800 =200

    Invalid vote in Block B 2017 is 2400- 2200 = 200

    hence this statement is correct 

3. Registered vote in A block = 3600

    Registered vote in B block = 6400

     ⇒ (3600 / 6400 )× 100

     ⇒ 56.25% 

     Hence statement 3 is also correct.

Valid vote block A in 2015 and 2017 is 

⇒ 1200 + 950 = 2150

Total registered vote in block B in 2015 and 2017 is 

⇒ 1800 + 2400 = 4200

Difference = 4200 - 2150

⇒ 2050

Hence 2050 is the correct answer.

Shortcut Trick

Gopi starts 4 hours before Kishan (10:00 A.M. to 2:00 P.M.).

Initial distance gap = Speed of Gopi × Time lead = 3 × 4 = 12 units.

Relative speed (same direction) = 5 − 3 = 2 units/hr.

Time to overtake = Distance gap ÷ Relative speed = 12 ÷ 2 = 6 hours.

Overtaking time = 2:00 P.M. + 6 hours = 8:00 P.M.

∴ The correct answer is 8:00 P.M.

Alternate Method

Given:

Speed of Gopi (S_G) = 3x, Speed of Kishan (S_K) = 5x.

Time difference = 2:00 P.M. − 10:00 A.M. = 4 hours.

Formula Used:

Distance = Speed × Time | Relative Speed = S₂ − S₁ (Same direction)

Calculations:

⇒ Distance covered by Gopi in 4 hours = 3x × 4 = 12x.

⇒ Relative speed = 5x − 3x = 2x.

⇒ Time required to cover the gap = 12x ÷ 2x = 6 hours.

⇒ Meeting time = Kishan's starting time + 6 hours.

⇒ Meeting time = 2:00 P.M. + 6 hours = 8:00 P.M.

∴ The correct answer is 8:00 P.M.

Additional Information

Relative Speed Concept

When two objects move in the same direction, relative speed is the difference of their speeds (S₁ − S₂). When they move in opposite directions, it is the sum (S₁ + S₂).

Meeting Time Formula

Meeting Time = [Initial Distance Gap] ÷ [Relative Speed]. This is applied from the moment the second person starts moving.

Proportionality of Speed and Time

For a constant distance, Speed is inversely proportional to Time (S₁/S₂ = T₂/T₁).

Shortcut Trick

Perimeter of Rectangle = 2 × (12 + 16) = 56 cm.

Side of Square = 56 ÷ 4 = 14 cm.

Radius of Semi-circle (r) = Side ÷ 2 = 14 ÷ 2 = 7 cm.

Perimeter of Semi-circle = (π + 2)r = (22/7 + 2) × 7 = 36 cm.

∴ The correct answer is 36 cm.

Alternate Method

Given: Length (L) = 12 cm, Breadth (B) = 16 cm.

Formulas: Perimeter of Rectangle = 2(L + B); Perimeter of Square = 4 × Side; Perimeter of Semi-circle = πr + 2r.

⇒ Perimeter of Rectangle = 2(12 + 16) = 2(28) = 56 cm.

⇒ Perimeter of Square = 4 × Side = 56 cm.

⇒ Side of Square = 56 ÷ 4 = 14 cm.

⇒ Diameter of Semi-circle (d) = Side of Square = 14 cm.

⇒ Radius of Semi-circle (r) = 14 ÷ 2 = 7 cm.

⇒ Perimeter of Semi-circle = (π × 7) + (2 × 7) = (22/7 × 7) + 14 = 22 + 14 = 36 cm.

∴ The correct answer is 36 cm.

Additional Information

Perimeter of Semi-circle

The boundary of a semi-circle consists of the curved arc (πr) and the straight diameter (2r). Perimeter = πr + 2r = r(π + 2).

Area of Semi-circle

The area of a semi-circle is exactly half the area of a full circle: Area = (1/2)πr².

Properties of Square and Rectangle

For a given perimeter, a square encloses a larger area than a rectangle of any other dimensions.

Shortcut Trick

Since the Principal is same, SI is directly proportional to Rate × Time.

SI_A : SI_B = 120 : 100 = 6 : 5

(x × 6) / ((x − 2) × 7) = 6 / 5

5x = 7x − 14 ⇒ 2x = 14 ⇒ x = 7

∴ The correct answer is 7%.

Alternate Method

Given: Principal (P) = ₹20,000 for both. Scheme A: Rate = x%, Time = 6 years. Scheme B: Rate = (x − 2)%, Time = 7 years. SI_A = 1.2 × SI_B.

Formula Used: Simple Interest (SI) = (P × R × T) / 100

⇒ SI_A = (20000 × x × 6) / 100 = 1200x

⇒ SI_B = (20000 × (x − 2) × 7) / 100 = 1400(x − 2)

⇒ According to question: 1200x = 1.2 × 1400(x − 2)

⇒ 1200x = 1680(x − 2)

⇒ 120x = 168x − 336

⇒ 48x = 336

⇒ x = 336 / 48 = 7

∴ The correct answer is 7%.

Additional Information

Simple Interest Relationship

When the Principal is constant, the ratio of Simple Interest for two cases is equal to the ratio of the product of their respective Rates and Time periods (R₁T₁ : R₂T₂).

Effective Rate of Interest

The total interest percentage earned over T years at R% per annum is calculated as (R × T)%. This is often called the Net Effective SI percentage.

Let the scheme have x rupees invested in CI for 2 years at 20% per annum 

Overall rate of interest is = 20 + 20 + 20× 20/100

⇒ 20+20+4 = 44% 

Interest is 44X %

Scheme B is invested at 2x in SI for 3 years at 10% per annum 

overall rate of interest is 3×10= 30%

⇒ 30X × 2 = 60x% 

Then required difference is = 60X% - 44X% = 16X% 

⇒ 16X % =Rs 2400

⇒ X = Rs 15000

Hence Rs 15000 is the correct answer

Shortcut Trick

Let Sakshi age be S. Then Anjali = S − 7 and Vikas = (S − 7) + 5 = S − 2.

Ratio Vikas : Sakshi = (S − 2) : S = 9 : 10.

Difference in ratio parts = 10 − 9 = 1 unit. Difference in actual age = S − (S − 2) = 2 years.

1 unit = 2 years ⇒ Sakshi = 10 × 2 = 20 years.

Anjali age = 20 − 7 = 13 years.

∴ The correct answer is 13 years.

Alternate Method

Given:

Vikas = Anjali + 5

Anjali = Sakshi − 7

Vikas : Sakshi = 9 : 10

Calculations:

⇒ Let Sakshi = 10x and Vikas = 9x.

⇒ Anjali = Sakshi − 7 = 10x − 7.

⇒ Vikas = Anjali + 5 = (10x − 7) + 5 = 10x − 2.

⇒ Equating Vikas: 9x = 10x − 2

⇒ x = 2.

⇒ Sakshi age = 10 × 2 = 20 years.

⇒ Anjali age = 20 − 7 = 13 years.

∴ The correct answer is 13 years.

Additional Information

Ratio and Proportions in Ages

If the ratio of ages is a:b and the numerical difference is D, then the ages are [a × D/(b−a)] and [b × D/(b−a)].

Age Gap Consistency

The difference between the ages of two persons remains constant regardless of the number of years passed or preceding.