Speed of the train = x kmph

Length of the platform = 120m

Time taken by the train to cross the platform = 16 seconds

Length of the both trains = y m

( y + 120)/(x ×  (5/18)) = 16

(y + 120) = 5x/18 ×  16

(y + 120) = 40x/9

x = (y + 120)×  9/40

Again,

(y + 120) /(108 ×  5/18) = 40/3

(y + 120)/30 = 40/3

(y + 120) = 400

y = 280m

x = (280 + 120) ×  9/40 = 90kmph

Hence, option(2) is correct.

Given:

A's time = 10 days,

B's time = 20 days,

C's time = 30 days,

Total earning = Rs. 1,100

Concept Used:

Work done is inversely proportional to time

Calculation:

⇒ A's work/day : B's work/day : C's work/day = 1/10 : 1/20 : 1/30 = 6 : 3 : 2

⇒ Earnings of A and C = (6 + 2)/11 ×  Rs. 1,100 = Rs. 800

⇒ Earnings of B = 3/11 × Rs. 1,100 = Rs. 300

⇒ Difference = Rs. 800 - Rs. 300 = Rs. 500

Therefore, the total earnings of A and C exceed the earnings of B by Rs. 500.

∴ Option 4 is the correct answer.

Formula used:

% change in revenue = (New revenue - Initial revenue) / Initial revenue] × 100

Calculation:

Let's assume the initial price of the product is 100 Rs & initial items sold out be 100 units.

New price = 100 - (12% of 100) = 100 - 12 = 88 Rs.

Initial number sold increase = 100

New number sold = 100 + (24% of 100) = 100 + 24 = 124 units

Initial total revenue = Initial price × Initial number sold

⇒ 100 × 100 = 10,000 Rs

New total revenue = 88 × 124 = 10,912 Rs.

% change in revenue = (New revenue - Initial revenue) / Initial revenue] × 100

⇒ [(10,912 - 10,000) / 10,000] × 100

⇒  [912 / 10,000] × 100 = 9.12%

Therefore, the effect on total revenue is an increase of approximately 9.12%.

Formula Used:

X% = X/100

Calculation:

(120% of 675) + 92 = (? % of 1240) + 716

⇒ 810 + 92 = 12.4 × ? + 716

⇒ 902 - 716 = 12.4 × ?

⇒ 186/12.4 = ? = 15

∴ The correct answer is 15

Given:

Selling price = ₹943

Discounts = 8%, 18%

Concept:

The effective selling price after consecutive discounts of x% and y% on the marked price is (100 - x)(100 - y)% of the marked price.

Calculation:

Let the marked price be 'M'

⇒ 0.82 × 0.92 × M = 943

⇒ M = 943/(0.82 × 0.92)

Therefore, the marked price of the watch is ₹1,250.

Given:

Total workers = 50

Wages of each man = Rs. 95

Wages of each woman = Rs. 70

Total wages = Rs. 4100

Concept used:

Total wages = Wages per head × Total number of workers

Calculation:

Let, number of men = a, and number of women = b

According to the question,

a + b = 50

⇒ b = 50 - a     ---(1)

95 × a + 70 × b = 4100

⇒ 95a + 70(50 - a) = 4100

⇒ 95a + 3500 - 70a = 4100

⇒ 25a = 4100 - 3500

⇒ 25a = 600

⇒ a = 600/25 = 24

∴ The number of men is 24.

Given:

Principal = Rs.10101, Time = 3 years, Rate = 9%

Formula used:

A = P(1 + r/100)ⁿ

Calculation:

A  = P(1 + r/100)n 

⇒ A = 10101[(1 + 9/100)³

⇒ A = 10101 × (109/100) × (109/100) × (109/100)

⇒ A = 13081.08

CI = 13081.08 - 10101 = 2980

∴ The answer is 2980.

Given:

Subsidy = 21%

Formula used:

Required angle = (360/100) × given percentage

Calculation:

Required angle = (360/100) × given percentage

⇒ subsidy angle = (360/100) × 21

⇒ subsidy angle = 75.6°

∴ The central angle for subsidy is 75.6°

Given:

The profit made by selling an article for Rs. 4,400 is equal to the amount of loss incurred on selling the same article for Rs. 3,600

Formula used:

Profit = selling price - cost price

Profit%  = Profit × 100/cost price.

Calculation:

let cost price be Rs. X

According to the question:

(4400 - X) = (X - 3600)

⇒ 8000 = 2X

⇒ X = 4000

if sp = 4800

Then, Profit = selling price - cost price

⇒ Profit = 4800 - 4000 = Rs.800

⇒ Profit % = Profit × 100/cost price

⇒ Profit = (800 × 100)/4000 = 20%

∴ The profit percent is 20%.

Given:

Selling Price = Rs. 3825

Discount = 25%

Formula used:

MRP = SP × 100/(100- D%)

Calculation:

MRP = SP × 100/(100- D%)

⇒ 3825 × 100/(100- 25)

⇒ 3825 × 100/75 = Rs 5100

∴ The Marked Price of an article is Rs 5100.