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Given:

Distance travel in 3 hours (Upstream) = 27 km

Distance travel in 3 hours (Downstream) = 99 km

Concept Used:

Upstream Speed = B - S

Downstream Speed = B + S

Time (T) = Distance (D)/Speed(S)

B = Speed of Boat

S = Speed of Stream

Calculation:

According to the question, we get

27/(B - S) = 3

⇒ B - S = 9 km/h  ---(i)

99/(B + S) = 3

⇒ B + S = 33 km/h  ---(ii)

From (i) and (ii), we get

B = 21 km/h

S = 12 km/h

According to the question, we get

Total Time taken = Time taken in Downstream + Time taken in Still water

⇒ {66/(21 + 12)} + (42/21)

⇒ (66/33) + (42/21) 

⇒ (2 + 2) hours

⇒ 4 hours

∴ The total time taken by boat is 4 hours.

Given:

If Raushan got 25% marks and failed by 64 marks and he had 40% marks he would have secured 32 marks more than the pass marks.

Formula used:

If the passing marks is 224 and total marks is 640,

Percentage passing marks = (Passing marks/Total marks) × 100

Calculation:

Let the total marks = x

According to question,

X × 25% + 64 = X × 40% - 32

⇒ X × 40% - X × 25% = 64 + 32

⇒ X × 15% = 96

⇒ X × (15/100) = 96

⇒ X = 640

So, passing marks = X × 25% + 64 = 640 × 25% + 64 = 640 × (25/100) + 64 = 224 marks

Percentage pass marks = (224/640) × 100 = 35%

∴ Percentage of pass marks is 35%

Shortcut Trick

25% + 64 = 40% – 32

⇒ 15% = 96

⇒ 100% = (96/15%) × 100%

⇒ 100%  = 640

And, 10% = 64

Percentage of pass marks = 25% + 64

⇒ 25% + 10% = 35%

∴ Percentage of pass marks is 35%

Given:

Discount = Rs. 100

Shopkeeper earns profit = 140%

Profit% if sold at no discount = 220%

Calculation:

Let the CP be 100%

SP if profit is 140% = 240%

SP if profit is 220% = 320%

Difference in SP = Discount of Rs. 100

So, 220%  – 140% = Rs. 100

⇒ 80% = Rs. 100

Then 100% = Rs. (100/80) × 100

⇒ Rs. 125

∴ CP of the article is Rs. 125

Given:

Principal = Rs. 14000, S.I. = Rs. 1260, Rate= 3% per annum, Time = t years

Formula used:

S.I. = (P × R × T)/100

C.I. = P[(1 + (r/100))^t – 1]

Calculation:

1260 = (14000 × 3 × t)/100

⇒ t = 3 years

C.I. = 14000 [(1 + (10/100))³ – 1]

⇒ 14000 [(11/10)³ – 1]

⇒ 14000 × (331/1000)

⇒ Rs.4634

Given:

A + B = 45,000

 C = 30,000 after 3 months

Calculation:

A : B = 2 : 3

⇒ Investment of A = (2 / 5) × 45,000

⇒ Investment of A = 18,000

⇒ Investment of B = 45,000 – 18,000

⇒ Investment of B = 27,000

Now, calculating profit sharing ratio

⇒ (18,000 × 12) : (27,000 × 12) : (30,000 × 9)

⇒ 24 : 36 : 30

⇒ 12 : 18 : 15

⇒ 4 : 6 : 5

∴ A, B and C will share profit in ratio of 4 : 6 : 5

 

A : B : C

⇒ (45,000 × 2 × 12 / 5) : (45,000 × 3 × 12 / 5) : (30,000 × 9)

⇒ 24 : 36 : 30

⇒ 12 : 18 : 15

∴ A, B and C will share profit in ratio of 4 : 6 : 5

Given:

Calculation:

Total number of patients recovered from covid-19 in April:

⇒ 150 + 190 + 240 + 225

⇒ 805

Total number of patients recovered from covid-19 in March:

⇒ 220 + 120 + 250 + 275

⇒ 865

The ratio between the total number of patients recovered from covid-19 in April to March

⇒ 805 : 865

⇒ 161 : 173

∴ The ratio between the total number of patients recovered from covid-19 in April to March is 161 : 173.

Given:

Calculation:

As we can see in the appropriate table, there is no continuous decrease in the number of patients recovered from covid-19 in all the states except Uttar Pradesh.

The number of patients who recovered from covid-19 in Uttar Pradesh

February to May = 290 > 250 > 240 > 220

∴ There is a steady decrease in the number of patients who recovered from covid-19 in Uttar Pradesh.

Given:

 

Calculation:

Total number of patients who recovered from Covid-19 in Madhya Pradesh in four months

⇒ 270 + 120 + 190 + 220

⇒ 800

The average number of patients who recovered from Covid-19 in Madhya Pradesh in four months:

⇒ 800/4

⇒ 200

∴ The amount of the average number of patients recovered from Covid-19 in Madhya Pradesh in four months is 200.

Given:

 

Calculation:

 The number of patients recovered from Covid-19 in all moths in Punjab:

⇒ 175 + 275 + 225 + 125 = 800

 The number of patients recovered from Covid-19 in all moths in Rajasthan:

⇒ 200 + 220 + 150 + 130 = 700

The difference between the number of patients recovered from Covid-19 in all moths in Punjab and Rajasthan:

⇒ 800 – 700

⇒ 100

∴ The difference between the number of patients recovered from Covid-19 in all months in Punjab and Rajasthan is 100.

Given:

The number of patients recovered from Covid-19 in Punjab in February 2021 = 175

The number of patients recovered from Covid-19 in Uttar Pradesh in February 2021 = 290

Calculation:

The number of patients in Uttar Pradesh is more than the number of patients in Punjab in February:

⇒ 290 – 175 = 115

The percentage of the number of patients in Uttar Pradesh is more than the number of patients in Punjab in February:

⇒ 115/290 × 100

⇒ 39.65%

⇒ ≈ 40%

∴ The number of patients recovered from Covid-19 in Punjab in February is ≈ 40% less than the number of patients recovered from Covid-19 Uttar Pradesh in February.