Given:

5 women can complete a work in 8 days and 8 children take 10 days to complete the work.

Formula used:

If a person can do a piece of work in days then that person's 1 day's work = 1/n

Calculations:

5W × 8 = 8C × 10

W/C = 2/1

Let the efficiency of women is 2 and children is 1.

Total work - 5 × 2 × 8 = 80

The work done by 2 women and 4 children = 2W + 4C

2 × 2 + 4 × 1 = 8

Number of days = 80/8 = 10 days.

∴ The answer is 10 days.

Given:

Let the principal be Rs 'P'

Time = 1 1/2 year = 3/2 years

Rate of interest = 8 %

Concept Used:

Simple interest = (P x T x R)/100

Amount at the rate of compound interest = P(1 + r/100)ⁿ

Compound Interest = Amount - Principal

(i) Simple interest = (P x T x R)/100

= (P x 3 x 8)/(2 x 100)

= 3P/25

(ii) Amount at the rate of compound interest = P(1 + r/100)ⁿ

= P(1 + 4/100)³

= P(26/25)3

= 17576P/15625

Compound Interest = (17576P/15625) - P

= 1951P/15625

Difference between the compound and simple interests = Rs 228

(1951P/15625) - (3P/25) = 228

(1951P/15625) - (1875P/15625) = 228

(76P/15625) = 228

P = 3 × 15625 = Rs. 46875

Therefore, the sum lent is Rs 46875.

Given:

Speed = 108 km/h

Time = 3 h

Formula:

Distance = Speed × Time

Solution:

The distance covered by the car is 108 × 3 = 324 km.

If the speed is reduced by 27 km/h, the new speed is 108 - 27 = 81 km/h.

The new time taken by the car to cover the same distance is 324/81 = 4 h.

Therefore, the time taken by the car to cover the same distance will be 4 h.

The answer is 4 h.

Given

The marke price is 25% more than the cost price.

The desired profit is 10%.

Concept:

MP/CP = (100 + Profit%)/(100 - Discount%)

Calculation:

MP/CP = (100 + Profit%)/(100 - Discount%)

⇒ MP is 25% more than CP.

⇒ 5/4 = (100 + 10)/(100 - Discount%)

⇒ 5/4 = (110)/(100 - Discount%)

⇒ 100 - Discount% = 88

⇒ Discount% = 12 

Therefore, a 12% discount on the selling price should be given to earn a 10% profit.

Given

Marked price of sofa = ₹18,000

Discount rates = 10%, 5%, 2%

Concept:

Successive Discount

Calculation:

After first discount, price = 90% of ₹18,000 = ₹16,200

⇒ After second discount, price = 95% of ₹16,200 = ₹15,390

⇒ After third discount, price = 98% of ₹15,390 = ₹15,082.20

Therefore, the net selling price of the sofa set is ₹15,082.20.

Given

24 women work time: 16 days

Number of new women: 32

Concept:

Direct proportionality of work to workers.

Calculation:

⇒ Since work is proportional to the number of workers, 24 women × 16 days = 32 women × x days

⇒ Solving for x, we get x = (24 × 16)/32 = 12 days

Hence, 32 women will complete the same work in 12 days.

Given data:

Two numbers = 4, 900

Concept: The mean proportional between two numbers a and b is √(ab).

Solution:

⇒ Mean proportional = √(4 x 900) = 60

Hence, the mean proportional between 4 and 900 is 60.

Given:

The total score of the batsman: 96 runs

Score from boundaries: 2 x 4 = 8 runs

Score from sixes: 6 x 6 = 36 runs

Concept Used: Percentage = (part / total) x 100

Solution:

Runs made by running between the wickets = Total score - score from boundaries - score from sixes = 96 - 8 - 36 = 52 runs

Percentage of score made by running = (52 / 96) x 100 = 54.16%

Therefore, the percentage of his total score that he made by running between the wickets is 54.16%.

Given:

Akhil, Sahil, and Amit together can do the work in 64 days

Akhil and Sahil can do the work in 80 days

Concept Used:

The total work is the same in both cases. The time taken by Amit alone can be found by subtracting the time taken by

Akhil and Sahil from the time taken by all three.

Solution:

⇒ Amit's 1 day work = (1/64 - 1/80)

⇒ Amit's time to complete the work = 1 / (1/64 - 1/80)

⇒ Amit's time to complete the work = 320 days

Therefore, Amit can do the same work in 320 days.

Given:

Principal amount (P) = Rs. 1,875

Interest rate (r) = 4%

Amount (A) = Rs. 2,028

Formula:

Where:

A is the amount after interest

P is the principal amount

r is the interest rate

t is the time period

Solution:

2028 = 1875(1 + 4/100)^t

(26/25)² = (1 + 4/100)t

(26/25)2 = (26/25)^t

t = 2 years

Therefore, the time period is 2 years.