I. 3x² + 2x – 21 = 0

⇒ 3x² + 9x – 7x – 21 = 0

⇒ 3x(x + 3) – 7(x + 3) = 0

⇒ (3x – 7) (x + 3) = 0

⇒ x = 7/3 or -3

II. 3y² – 19y + 28 = 0

⇒ 3y² – 12y – 7y + 28 = 0

⇒ 3y(y – 4) – 7(y – 4) = 0

⇒ (3y – 7) (y – 4) = 0

⇒ y = 7/3 or 4

Comparison between x and y (via Tabulation):

∴ x ≤ y

I. x² – 22x + 120 = 0

⇒ x² – 12x – 10x + 120 = 0

⇒ x(x – 12) – 10(x – 12) = 0

⇒ (x – 12)(x – 10) = 0

Then, x = 12 or x = 10

II. y² – 27y + 182 = 0

⇒ y² – 13y – 14y + 182 = 0

⇒ y(y – 13) – 14(y – 13) = 0

⇒ (y – 13)(y – 14) = 0

Then, y = 13 or y = 14

∴ We can clearly see that x < y

The quantity of cereals produced in 2021 + 2022 = 850 tonnes

The quantity of cereals produced in 2019 + 2020 = 478 tonnes

Let the quantity of cereals produced in 2019 = x tonnes

Therefore, the quantity of cereals produced in 2021 = x + 300 tonnes

Let the quantity of cereals produced in 2020 = y tonnes

Therefore, the quantity of cereals produced in 2022 = y + 72 tonnes

So, x + y = 478 ...(i)

And, x + 300 + y + 72 = 850

⇒ x + y = 478 ...(ii)

Both the equations are same so, the data is insufficient.

Hence, the correct answer is CND.

The quantity of wheat produced in 2021 + 2022 = 420 tonnes

The quantity of pulses produced in 2021 + 2022 = 900 tonnes

Required difference = 900 - 420 = 480 tonnes

Hence, the correct answer is 480 tonnes.

The total quantity of rice produced in 2021 + 2022 = 685 tonnes

The quantity of rice produced in 2022 = 270/1.20 = 225 tonnes

Let the quantity of unsold rice in 2021 = x tonnes

The quantity of rice sold in 2021 = 347 tonnes

Therefore, (347 + x) + 225 = 685

⇒ x = 113 tonnes

Hence, the correct answer is 113 tonnes.

The total quantity of maize produced in 2017 + 2018 = 448 tonnes

The ratio of the quantities of maize produced in 2017 to that in 2018 = 29 : 27

The decrease in the quantity of the production of maize from 2017 to 2018 = (2/56) × 448 = 16 tonnes

Hence, the correct answer is 16 tonnes.

Average production of each of the five crops in 2018 = 347.4 tonnes

Average production of each of the five crops in 2017 + 2018 = (556 + 855 + 448 + 581 + 566)/5 = 601.2 tonnes

The average production of each of the crops in 2017 = 601.2 - 347.4 = 253.8 tonnes

Hence, the correct answer is 253.8 tonnes.

Shortcut Trick

The age of new member is less than the age of old member

So, the average will be decreased after replacement.

Now, Difference in ages of person left and joined = 60 - 33 = 27

Effect of replacement on average = 27/9 = 3 years

Hence, The average will decrease by 3 years.

Alternate Method

Given:

Average age of team = 45 years

Retirement age = 60 years

Age of new member = 33 years

Formula used:

Average = (Sum of observations)/(Number of observations)

Calculation:

Previous um of age of team = 9 × 45 = 405

Total age after replacement = 405 - 60 + 33 = 378

Mew average age of team = 378/9 = 42

Effect of retirement = 45 - 42 = 3 years (Decrease)

Hence the average age will decrease by 3 years.

Let the total population of the village initially was 100x

Now, 15% people died and 230 babies were born

∴ Population of the village now = 85x + 230

35% people from that village migrated to cities

∴ Present population of the village = (65/100) × (85x + 230)

According to the question

⇒ (65/100) × (85x + 230) = 4680 

⇒ 85x + 230 = 4680 × (100/65)

⇒ 85x + 230 = 7200 

⇒ x = 82

∴ Population of the village = 82 × 100 = 8200

Number of people who died in the previous year = (15/100) × 82 = 1230

Given:

Samar lent Rs. 8800 in two different schemes at 11% and 7% per annum simple interest respectively

Formula used:

Simple Interest = {Sum (P) × rate of interest (r) × time (t)}/100

Calculation:

Let the sum at 11% and at 7% be x and (8800 – x) respectively

S.I at 11% rate = 11 × x × 6/100 = 66x/100

S.I at 7% rate = 7 × (8800 – x) × 6/100

⇒ 42 × (8800 – x)/100

⇒ 66x/100 + 42 × (8800 – x)/100 = 4824

⇒ 24 × x = 482400 – 369600 = 112800

⇒ x = 4700

∴ The sum he lent at a S.I rate 11% per annum is Rs. 4700

Shortcut Trick

Formula Used:

Alligation method,

Calculation:

The S.I rate = (4824 × 100)/(8800 × 6) = 201/22

The sum lent at S.I rate 11%

⇒ 47 × 8800/88 = 4700

∴ The sum lent at a S.I rate 11% per annum is Rs. 4700