Given:

The area enclosed between the circumferences of two concentric circles = 16π cm²

The ratio of their radii = 5 : 3

Formula used:

Area of circle = πr²

Calculation:

Let the radius be R = 5x and r = 3x

According to the question

⇒ πR² - πr² = 16π

⇒ π(R² - r²) = 16π

⇒ R² - r² = 16

⇒ (5x)² - (3x)² = 16

⇒ 25x² - 9x² = 16

⇒ 16x² = 16

⇒ x = 1

Now, outer circle R = 5x = (5 × 1) = 5 cm

The area of outer circle = π(5)² = 25π cm²

∴ The required area is 25π cm²

Given:

A train covers a certain distance at a speed of 80 km/h in 6 hours

Formula Used:

Hence, The speed of the train to cover the same distance in 5 hours is 96 km/h.

Given:

The winning candidate received 15744 votes, which is 48% of the electorate.

The only other candidate received 22% of the electorate.

Calculations:

Let the total votes be x

According to the question,

48% of x = 15744

⇒ x = (15744/48) × 100

⇒ x = 32800

Now votes received by other candidates

22% of 32800

⇒ 22 × 328 = 7216 votes

Total votes received = 15744 + 7216 = 22960

No. of people did not voted = 32800 - 22960 = 9840

∴ The number of members who did NOT vote is 9840.

Given:

Amit, Bipin and Kaithi can complete a piece of work in 20, 30 and 60 days

Concept used:

Total work = Efficiency of the workers × time taken by them

Calculation:

LCM of 20, 30, and 60 is 60 i.e total work

Efficiency of Amit = 60/20 = 3 units/day

Efficiency of Bipin = 60/30 = 2 units/day

Efficiency of Kaithi = 60/60 = 1 units/day

Now,

1st two days only Amit works

So, amount of work done = 6 units

3rd day Bipin and Kaithi join

So, total work on 3rd day = 3 + 2 + 1

⇒ 6 units

So,

In 3 days total 12 units of work is completed

So, effective efficiency = 12/3 = 4 units/day

Time = 60/4 = 15 days

∴ Required answer is 15 days.

Given:

Manish buys an old car for Rs. 5,300 and spend Rs. 1,000 on its repairs

His selling price = Rs. 7000

Concept used:

Profit = Selling price - cost price

Profit% = (Profit/Cost price) × 100

Calculation:

His net cost price = 5300 + 1000

⇒ Rs. 6300

Now,

His profit = 7000 - 6300

⇒ Rs. 700

Profit % = (700/6300) × 100

GIVEN:

P grazes 15 cows for 4 months, Q grazes 21 cows for 3 months and R grazes 24 cows for 5 months.

Rent for a year = Rs. 3240

CONCEPT:

Rent will be shared according to the number of cows and time for which the cows graze.

CALCULATION:

According to the given data:

Ratio in which the rent will be shared among P, Q and R

= (15 × 4) : (21 × 3) : (24 × 5)

= 60 : 63 : 120

= 20 : 21 : 40

Hence,

Calculation:

State T has witnessed two times increase in 2016 and 2017 or 2020 and 2021.

State A has witnessed two times increase in 2019 and 2020

State M has witnessed two times increase in 2019 and 2020

State K has witnessed two times increase in 2020 and 2021

So, total 4 states witnessed an increase in the amount of annual rainfall continuously for two times in immediate years

∴ The required answer is 4.

Given:

Marked Price = Rs. 550

It is sold for Rs. 428.45 after giving two successive discounts of 18% and x% on the marked price. 

Concept used:

Selling price = Marked Price - Marked Price × Discount%

Calculation:

After giving the first 18% discount the price becomes

⇒ 550 - 550 × 18%

⇒ 550 - 99

⇒ Rs. 451

According to the question,

451 - 451 × x% = 428.45

⇒ 451 × x% = 451 - 428.45

⇒ 451 × x% = 22.55

⇒ x% = 22.55/451

⇒ x = 0.05 × 100

⇒ x = 5

Now, 2x = 2 × 5

⇒ 10

∴ The value of 2x is 10.

Calculation:

Total % of D1 and D4 = 12 + 14

⇒ 26%

Total % of D2 and D7 = 11 + 11

⇒ 22%

Difference = 26% - 22%

⇒ 4%

Difference in amount = 4962000 × 4%

⇒ 198480

∴ The required answer is Rs. 1,98,480.

Given:

CP = Rs. 3,910, SP = Rs. 4,590, and Total articles = 17

Formula used:

Hence, there is a profit of approx 17% per article.