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Given:

The ratio of the salaries of Ravi and Sarita is 3 ∶ 5.

If the salary of each is increased by ₹ 5,000, the new ratio becomes 29 ∶ 45.

Formula Used:

Initial salaries: R = 3x and S = 5x.

New salaries: R + 5000 and S + 5000.

New ratio: (R + 5000) / (S + 5000) = 29/45.

Calculation:

Substituting the values of R and S in the new ratio equation:

(3x + 5000) / (5x + 5000) = 29 / 45

Cross multiplying to solve for x:

⇒ 45 × (3x + 5000) = 29 × (5x + 5000)

⇒ 135x + 225000 = 145x + 145000

⇒ 145x - 135x = 225000 - 145000

⇒ 10x = 80000

⇒ x = 8000

Now, finding the current salary of Sarita:

S = 5x = 5 × 8000

S = 40000

The present salary of Sarita is ₹ 40,000.

Shortcut Trick

Shortcut Trick

Distance covered by Train X in 1 hour (11 a.m. to 12 noon) = 65 km.

Remaining distance at 12 noon = 390 − 65 = 325 km.

Relative speed (opposite direction) = 65 + 35 = 100 km/h.

Time taken to meet after 12 noon = 325 ÷ 100 = 3.25 hours.

0.25 hours = 0.25 × 60 = 15 minutes. So, 3 hours 15 minutes after 12 noon.

∴ The correct answer is 3:15 p.m.

Alternate Method

Given:

Total Distance = 390 km

Speed of Train X (S₁) = 65 km/h (Starts at 11 a.m.)

Speed of Train Y (S₂) = 35 km/h (Starts at 12 noon)

Formula Used:

Distance = Speed × Time

Relative Speed (Opposite Direction) = S₁ + S₂

Calculations:

⇒ Distance covered by Train X before Train Y starts (1 hour) = 65 × 1 = 65 km

⇒ Remaining distance to be covered relatively = 390 − 65 = 325 km

⇒ Relative speed = 65 + 35 = 100 km/h

⇒ Time taken to meet = 325 ÷ 100 = 3.25 hours

⇒ 3.25 hours = 3 hours + (0.25 × 60) minutes = 3 hours 15 minutes

⇒ Meeting time = 12:00 noon + 3 hours 15 minutes = 3:15 p.m.

∴ The correct answer is 3:15 p.m.

Additional Information

Relative Speed Concept

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

Meeting Time Calculation

Always calculate the distance covered by the first object until the second object starts moving to find the effective distance for relative speed application.

Average Speed

For a journey with two equal distances at speeds a and b, Average Speed = 2ab ÷ (a + b).

Given : 

Pipe A can fill an empty tank in 6 h and pipe B in 8 h.

Both the pipes are opened at the same time and pipe A is closed after 2 hours.

Calculation:

Total work = LCM of (6, 8) = 24 unit

Efficiency of pipe A = 24/6 = 4 unit and efficiency of pipe B = 24/8 = 3 unit

In the 1^st two hours both pipes are opened, the work done = (4 + 3) × 2 = 14 unit

Remaining = (24 - 14) = 10 unit

Now, pipe B can do it in = 10/3 = \(3\frac{1}{3}\) hour

∴ The correct answer is \(3\frac{1}{3}\) hour

Given : 

P got 35% more votes then Q.

R got 25% more votes than Q.

Also P beats R by 1250 votes​.

Calculation:

Let's assume that  Q's vote count = x,

P's vote count =  1.35x and R's votes = 1.25x

We also know that P beats R by 1250 votes, then

⇒ 1.35x - 1.25x = 1250

⇒ 0.1x = 1250

⇒ x = 1250/0.1

⇒ x = 12500

So, Q got 12500 votes,

P got 1.35 × 12500 = 16875 votes

And R got 1.25 × 12500 = 15625 votes.

The total votes cast = 16875 + 12500 + 15625 = 45000 votes

Now, 80% of the voters voted, then

Total number of voters = 45000 / 0.80 = 56250

∴ The correct answer is 56250

Calculation : 

⇒ 2³ - 5⁰ = 8 - 1 - 7

∴ The correct answer is 7.

Given : 

P = Rs. 21300

Time = Rate 

SI = Rs.5325

Formula used : 

SI = (P × R × T)/100

Calculation : 

According to question,

Let the rate and time be x.

⇒ 5325 = (21300 × x²)/100

⇒ x² = 5325/213

⇒ x² = 25

⇒ x = + 5, - 5

∴ The correct answer is 5.

Shortcut Trick

Let the remainder in the first case be R₁ = 25.

When the number is doubled, the new remainder should be 2 × R₁ = 2 × 25 = 50.

However, the actual remainder is R₂ = 13.

The divisor (D) is the difference between the expected remainder and the actual remainder.

⇒ Divisor = (2 × R₁) − R₂ = 50 − 13 = 37.

∴ The correct answer is 37.

Alternate Method

Given:

Let the number be N and the divisor be D.

⇒ N = D × q + 25 (where q is the quotient)

Calculations:

⇒ 2N = 2(D × q + 25)

⇒ 2N = 2Dq + 50

Since 2N divided by D leaves a remainder of 13:

⇒ 50 = D × k + 13 (where k is some integer)

⇒ D × k = 50 − 13

⇒ D × k = 37

Since 37 is a prime number and the remainder (25) must be less than the divisor (D > 25):

⇒ D = 37

∴ The correct answer is 37.

Additional Information

Division Algorithm

Dividend = (Divisor × Quotient) + Remainder. The remainder must always be 0 ≤ Remainder < Divisor.

Remainder Theorem Property

If a number N leaves remainder R when divided by D, then kN leaves the same remainder as kR divided by D.

Finding Divisor from Two Remainders

If N₁ leaves R₁ and N₂ leaves R₂, and (N₁+N₂) leaves R₃ when divided by D, then D = R₁ + R₂ − R₃.

Given : 

CP = 12% below its cost

SP = 12% above its cost

Calculation :

Let the CP be 100.

So, Real CP = 88

Real SP = 112

Profit = 112 - 88 = 24

⇒ 24/88 × 100 = 2400/88

⇒ 27.27%

∴ The correct answer is 27.27%.

Given:

The radius of the cone is equal to the radius of the hemisphere

The height of the cone is equal to the height of the hemisphere

Formula used:

The curved surface area of the hemisphere = 2πr2

The curved surface area of the Cone = πrl

l = √ (h2 + r2)

Where 'l' is a slant height

Calculations:

Let the radius of the cone is equal to the radius of the hemisphere be r.

So the height of the cone, h = r.

According to the question,

The ratio of the areas of curved surfaces of hemispheres and cone

⇒ 2π × r2 :  π × r × l

⇒  2π × r2 :  π × r × √ (r2 + r2)

⇒  2π × r2  :  π × r × √ (2r2)

⇒  2 : \(\sqrt{2}\)

⇒  \(\sqrt{2}\) : 1

∴ The ratio of the areas of curved surfaces of hemisphere and cone is \(\sqrt{2}\) : 1.

Given :

Average of six consecutive numbers A, B, C, D, E and F is 62.

Formula used : 

Average = Sum of all observations/Number of observations

Calculation : 

Let the Numbers A, B, C, D, E, F be x, x + 1, x + 2, x + 3, x + 4, x + 5.

According to question,

⇒ x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 62 × 6

⇒ 6x + 15 = 372

⇒ 6x = 372 - 15 = 357

⇒ 6x = 357

⇒ x = 59.5

⇒ B = x  + 1 = 60.5

⇒ F = x + 5 = 64.5

Product of B and F = 60.5 × 64.5 = 3902.25

∴ The correct answer is 3902.25.