Calculation:

Income of P and Q  = 650 + 450 = 1100

Expenditure of S and T = 150 + 100 = 250

According to the question:

(1100 - 250)250 × 100

850/250 × 100

85 × 4 = 340%

∴ Option 4 is the correct answer.

Given: 

The difference between the 25% of a number and 30% of that number = 500

Calculation:

Let the number be X

According to the question, we have

(30% of X) - (25% of X) = 500

⇒ 5% of X = 500

⇒ X = (500 × 100)/5

⇒ X = 10000

Now,

20% of X = (20/100) × 10000

⇒ 2 × 1000

⇒ 2000

∴ The value of 20% of the number is 2000.

Given:

Ratio of three numbers = 7 : 3 : 5

Sum of the three numbers = 7200

Calculation:

Let the numbers be 7x, 3x and 5x

Then, according to the question,

7x + 3x + 5x = 7200

⇒ 15x = 7200

⇒ x = 480

⇒ 7x = 3360, 3x = 1440

7x + 3x = 4800

∴ Sum of the largest and smallest number = 4800

Given:

Gain on selling 24 items = SP of 4 items

Concept Used:

Calculation:

⇒ Let the SP of an item be Rs 100.

⇒ Total SP of 24 items = 24 × 100 = Rs 2,400

⇒ Gain = 4 × 100 = Rs 400

⇒ Cost Price of 24 items = 2400 – 400 = Rs 2,000

Therefore, the gain percentage is 20%.

Given:

3 men can complete the work = 32 days 

7 women can complete the work = 32 days 

Formula Used:

Work = time × efficiency 

Calculation:

⇒ Let the efficiency of men and women be M and W 

⇒ Work by men = work by women 

⇒ 3M × 32 = 7W × 32 

⇒ M : W = 7 : 3 

⇒ Total work = 3 × 7 × 32 = 672 units

The efficiency of man = 7 units per day, so the efficiency of 7 men = 7 x 7 = 49 units

similarly, the efficiency of woman = 3 units , so the efficiency of 5 women = 5 x 3 = 15 units

Work = time × efficiency

⇒ 7 Men and 5 women can do twice of work = (672× 2)/(49 + 15) = 1344/64 = 21 days

Given,

1 Divisor = 136

2 Divisor = 17

1 Remainder = 36

Formula Used:

Dividend = Divisor × Quotient + Remainder

Calculation -

Let the given number divided by 136 gives the quotient K and remainder 36

⇒ The given number = (136K + 36)

⇒ (17 × 8K) + (17 × 2) + 2

⇒ 17(8K + 2) + 2

Hence the given number is divided by 17 and the remainder will get = 2

Given:

Length of two train = 440 m and 160 m

Time = 120 seconds

Speed of one train = 50 m/s

Formula used:

When the two objects are moving in the same direction, then their relative speed is the difference of their speeds,.hence,

Time = (length of train (1) + length of train(2)/[(Speed of train(1) - Speed of train (2)]

Calculation:

Let the speed of other train be x m/s.

120 = (440 + 160)/(50 - x)

⇒120 = 600/(50 - x)

⇒ 6000 - 120x = 600

⇒ 5400 = 120x

⇒ 5400/120 = x

⇒ 45 m/s = x

∴ Speed of other train is 45 m/s

GIVEN:

Man speed increases to 11/6 times his original speed

Difference in time before and after increasing speed is 20 min

FORMULA USED:

Distance = Speed × Time

CALCULATION:

Let the distance be d

Let the original speed be 6x

New speed = 11/6 × 6x = 11x

Now, according to the given question we have

d/6x - d/11x = 20

⇒ ( 11d - 6d) /66x = 20

⇒ 5d/66x = 20

⇒ 5d = 1320x  ⇔ d = 264x

Now, original time = distance/ original speed

⇒ d/6x = 264x/6x = 44  minutes ......[d = 264x]

Hence, original time taken is 44 minutes.

Let the length of the cube be x cm

⇒ The length after 2 cm increase = x + 2 m

⇒ Initial volume = x³

⇒ Volume after increasing side = (x + 2)³

⇒ (x + 2)³ – x³ = 488

⇒ x³ + 6x² + 12x + 8 – x³ = 488

⇒ 6x² + 12x – 480 = 0

⇒ x² + 2x – 80 = 0

⇒ (x – 8) (x + 10) = 0

⇒ x = 8, -10

⇒ x = 8 cm