Calculation:

Let the marked price be Rs. 100

After discount price be = 100 × (1 - 20/100) = Rs 80

Let the price for which he has bought that object be Rs. y, Now from the problems statement

⇒ y (1 + 16/100) = 80

⇒ 1.16 y = 80

⇒ y = 80/1.16 = 68.96

Now, when an article is sold at M.P then

∴ Profit % = (100 - 68.96)/(68.96) × 100 = 45.01% or 45%

∴ Option 1 is the correct answer.

Given:

A chair is sold at a discount of 20%, then there is a profit of 20%.

Concept used:

Selling price = Cost price × (100 + Profit)%

Selling price = Marked price × (100 - Discount)%

Calculation:

Let the cost price be 100a

So, selling price = 100a × 120%

⇒ 120a

Now,

Marked price = 120a × (100/80)

⇒ 150a

New selling price = 150a × 70%

⇒ 105a

So, profit = 5a

Profit % = (5a/100a) × 100

⇒ 5%

∴ The required answer is 5%.

Given:

Two ratios are 3:7 and 5:9

Concept:

We have to equal any one of the ratio quantity

Calculation:

Multiply by 9 of first ratio

5:9 is the greatest ratio

∴ The Correct Answer is 5:9

Given:

x is directly proportional to y

x = 10 when y = 8

Concept/Formula Used:

If x is directly proportional to y, then x/y = k (constant).

Calculation:

k = x/y = 10/8 = 1.25.

When y = 36, x = k × y = 1.25 × 36 = 45.

Therefore, the value of x when y = 36 is 45.

Given:

9 ÷ [5 + 7 ÷ {9 + 9 ÷ (9 + 9 ÷ 4)}] = ?

Concept Used:

Given:

A train cover a distance of 3750 km in 25 hours

Formula used:

Speed = Distance/Time

Distance = Speed × Time

Calculation:

According to the question:

Speed = Distance/Time

⇒ Speed = 3750/25 = 150 km/hr

Now, new time will be 1 hour, then

Distance = Speed × Time

⇒ Distance = 150 × 1 = 150 km

∴ The average distance is 150 km.

Given:

The total distance = 300 km

The car takes time to cover 300 km = 5 hours

Formula Used:

Speed = Distance / Time.

Calculation:

Given:

A and B together finish the work in 8 days.

B and C together can do it in 12 days.

A, B, and C together can do this work in 6 days

Concept used:

Entire work = Work done each day (in Units) × Total time taken (in days)

Calculation:

LCM (8,12,6) = 24

Let the entire work be the LCM of 8, 12, 6.

So, the entire work is 24 units.

Now,

A & B together do = 24 ÷ 8 = 3 units each day

B & C together do = 24 ÷ 12 = 2 units each day

A, B & C together do = 24 ÷ 6 = 4 units each day

Then,

A + B = 3      ....(1)

B + C = 2      ....(2)

A + B + C = 4      ....(3)

Solving (1), (2), (3),

We get, C = 1, A = 2

So, A & C together do (2 + 1) = 3 units

Then, the time taken by A & C together to finish twice the work = {(24 × 2) ÷ 3} = 16 days

∴ In 16 days, A & C together will complete twice the work.

Given:

Sonu can do a work in 25 days and Kavita can do the same work in 20 days.

Together they work for 5 days and then Sonu leaves the work

Formula used:

If a person can do a work in x days, part of work done by that person in one day = 1/x

Calculations:

∴ The answer is 11 days.

Shortcut Trick

Concept use: 

Total work done = Efficiency × Total number of days

Calculation: 

Sonu and Kavita can do the same work in 25 days & 20 days respectively.

So, Total wok is LCM of (25, 20) = 100

Here, the efficiency of Sonu and Kavita is 4 & 5 respectively.

In 5 days their work done is 5 × (4 + 5) = 45

The remaining work is (100 - 45) = 55

The remaining work is done by Kavita in 55/5 = 11 days.

Given:

In a mixture, water and milk are in the ratio of 2 : 3.

Calculation:

Quantity of the water in 20 kg mixture = 20 × 2/5

⇒ 8 kg

Quantity of milk in 20 kg mixture = 20 × 3/5

⇒ 12 kg

In the new mixture ratio of water and milk = 1 : 1

So, water must be 12 kg

So, water needed to add = 12 - 8

⇒ 4 kg

∴ The required answer is 4 kg.