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Number of mangoes sold by company A in August 2024 = (120/100) × 650 = 780

Number of mangoes sold by company B in August 2024 = (140/100) × 200 = 280

So, new ratio will be = 780 : 280 = 39:14

Total number of mangoes sold from shop A in the present year (2023) = 500 + 650 + 750 + 800 + 500 = 3200

Total number of mangoes sold in next year will be = (220/100) ×  3200 = 7040

As the sales of mangoes except October and November remain same.

So,the number of mangoes sold in 2024 from July, August, and September = 500 + 650 + 750 = 1900

So, the number of mangoes sold in 2024 from October and November = 7040 – 1900 = 5140

Number of mangoes sold in 2024 in the month of November = 5140/2 = 2570

Hence, the total number of mangoes sold in the month of November for 2023 and 2024 = 500 + 2570 = 3070.

As per the data.

Total number of mangoes sold from company A = 500 + 650 + 750 + 800 + 500 = 3200

Total number of mangoes sold from company B = 150 + 200 + 300 + 400 + 500 = 1550

Hence, required ratio = 3200 : 1550 = 320 : 155 = 64 : 31

Given:

5 men and 3 women together or 9 men can cultivate a land in 60 days

Calculation:

According to the question,

(5m + 3w) = 9m

⇒ 3w = 4m

So, (8m + 9w) = 8m + 12m = 20m

9m can cultivate a land in 60 days

1m can cultivate a land in 60 × 9 days

20m can cultivate a land in (60 × 9)/20 days = 27 days.

Alternate Method(5m + 3w) × 60 = 9m × 60

⇒ m/w = 3/4

Total work = (5 × 3 + 3 × 4) × 60 = 27 × 60 =1620

Total efficiently of (8m + 9w) = 8 × 3 + 9 × 4 = 24 + 36 = 60

Required no of days = 1620/60 = 27 days

Shortcut Trick

Let the total salary be 100 units.

Remaining after 30% grocery = 70 units.

Expenses from remaining: 20% (Rent) + 50% (Loan) = 70%.

Savings from remaining = 30% of 70 = 21 units.

21 units = Rs. 14700 → 1 unit = Rs. 700 → 100 units = Rs. 70000.

∴ The correct answer is Rs. 70000.

Alternate Method

Given: Savings = Rs. 14700 | Grocery = 30% | Rent = 20% of remaining | Loan = 50% of remaining

Formula: Savings = Salary × (100 − %Spent₁)/100 × (100 − %Spent₂)/100

⇒ Let Salary be S.

⇒ Remaining after Grocery = S × (100 − 30)/100 = 0.70S

⇒ Total % spent from remaining = 20% + 50% = 70%

⇒ Savings from remaining = 100% − 70% = 30%

⇒ 30% of 0.70S = 14700

⇒ (30/100) × (70/100) × S = 14700

⇒ 0.21S = 14700

⇒ S = 14700 ÷ 0.21 = 70000

∴ The correct answer is Rs. 70000.

Additional Information

Remaining Balance Concept

When expenses are calculated on the remaining amount, use the multiplying factor method: Final = Initial × (1 − r₁/100) × (1 − r₂/100).

Successive Percentage Change

The overall percentage reduction from the original value is 100 − [100 × (1 − r₁/100) × (1 − r₂/100)].

Base Change Rule

Always identify if the percentage is of the total or of the remaining balance to avoid calculation errors.

Given:

Speed of train = 30 km/hr.

speed of man = 6 km/hr.

Time taken to cross the platform = 24 seconds

time taken to cross the man = 8 seconds.

 

Formula used:

Distance = speed x time

 

Calculation:

 

speed of the train relative to the man = 30 + 6 km/hr.

⇒ 36 × 5/18  m/s

⇒ 10 m/s

Distance travelled by the train in 8 seconds at this relative speed = 8 × 10 = 80m

Length of the train = 80m

 

Speed of the train = 30 km/hr. = 30 × 5/18 m/s

⇒ 25/3 m/s

 

distance travelled in 24 seconds = 24 × 25/3

⇒ 200m

This distance 200m covered is the sum of the length of the train and the length of the platform.

Length of train + length of platform = 200m

Length of platform = 200 - 80

⇒ 120m

 

∴The lengths of train and the platform are 80m and 120m respectively.

The correct answer is: 3

Given:

in 10 hours, John can go 30 km upstream and 44 km downstream.

in 13 hours, he can go 40 km upstream and 55 km downstream.

Formula used:

Time = distance/speed

Calculation:

let speed of john in still water i.e. boat = B

and the speed of stream = S

then, 30/B - S  +  44/B + S = 10     ----(1)

 &      40/B - S  +  55/B + S = 13     ----(2)

let 1/B - S = m     and    1/B + S = n

then, 30m + 44n = 10     ----(3)

and    40m + 55n = 13     ----(4)

by solving (3) and (4), we get,

m = 1/5 and n = 1/11

∴ B - S = 5   &  B + S = 11

by solving this, we get  2B = 16 

⇒ B = 8

∴ Speed of john in still water is 8 km/hr.

Given:

Average marks of a student in seven subjects = 75

Average marks in 6 subjects = 73

Calculations:

Total marks in seven subjects = 7 × 75 = 525

Now, excluding English

∴ Total marks in six subjects = 6 × 73 = 438

∴ Marks in English = 525 - 438

⇒ 87

Marks he scored in English is 87.

Given:

10 years ago, Ratio of age of Ram's father and Ram = 3 : 1

10 years later, Ratio of age of Ram's father and Ram = 2 : 1

Calculation:

Let 10 years ago Ram's age be x years.

then, 10 years ago the age of Ram's father = 3x years

The present age of Ram = (x + 10) years

And the present age of Ram's father = (3x + 10) years

According to the question,

3x + 10 + 10 = 2(x + 10 + 10)

⇒ 3x + 20 = 2(x + 20)

⇒ 3x + 20 = 2x + 40

⇒ 3x - 2x = 40 - 20

⇒ x = 20

Hence the present age of Ram = (20 + 10) years

⇒ 30 years.

∴ The present age of Ram is 30 years.

Given:

A basket contains 2 white, 3 red and 4 black balls, two balls are drawn at random

Concept used:

The classical definition of probability.

Formula used:

Probability = Favorable Outcome/Total Outcome.

P (E) = n(E)/n(S)

Calculation:

Total number of balls = 2 + 3 + 4

Let S be the sample space.

n(S) = Total number of ways of drawing 2 balls out of 9 

⇒ ⁹C₂

Let E = Event of drawing 2 balls, none of them is black

n(E) = Number of ways of drawing 2 balls, none of them is black

⇒ ⁵C₂

There are four black balls in the total nine balls. Total number of non-black balls = 9 - 4 = 5

P(E) = n(E)/n(S)

⁵C₂/⁹C₂

⇒ {(5 × 4)/(2 × 1)}/{(9 × 8)/(2 × 1)}

⇒ 10/36 = 5/18

∴ The probability of not any ball being drawn is black is 5/18.