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Rate of interest = 10% = 1/10.

For Compound Interest, the ratio of Principal (P) to Amount (A) for 1 year is 10 : 11.

For 3 years, the ratio P : A = 10³ : 11³ = 1000 : 1331.

Given Amount = 1331 units = ₹10,648.

1 unit = 10,648 ÷ 1331 = 8.

Principal = 1000 units = 1000 × 8 = ₹8000.

∴ The correct answer is ₹8000.

Alternate Method

Given:

Amount (A) = ₹10,648

Rate (R) = 10% per annum

Time (n) = 3 years

Formula Used:

A = P(1 + R/100)ⁿ

Calculations:

⇒ 10,648 = P(1 + 10/100)³

⇒ 10,648 = P(1 + 1/10)³

⇒ 10,648 = P(11/10)³

⇒ 10,648 = P × (1331 / 1000)

⇒ P = (10,648 × 1000) / 1331

⇒ P = 8 × 1000

⇒ P = ₹8000

∴ The correct answer is ₹8000.

Additional Information

Effective Rate of Interest

For a rate R, the effective CI rate for 3 years is [ (1 + R/100)³ − 1 ] × 100%. For 10%, it is 33.1%.

Difference between CI and SI

For 3 years: Difference = P(R/100)² × (3 + R/100). For 2 years: Difference = P(R/100)².

Half-Yearly Compounding

When interest is compounded half-yearly, the rate is halved (R/2) and the time period is doubled (2n).

Given:

Marked price of the computer = Rs. 80,000,

Selling price after two discounts = Rs. 65,280,

First discount = 15%

Concept Used:

Concept: Successive discounts are calculated individually on the new price.

Solution:

Let the second discount be 'x' percent.

Selling price after the first discount = Marked price - (15/100) × Marked price

Selling price after the first discount = 80,000 - (15/100) × 80,000 

⇒ 80000 - 12000 = Rs. 68000

Selling price after the second discount = Selling price after the first discount - (x/100) × Selling price after the first discount

Selling price after the second discount = 68000 - (x/100) × 68000

Selling price after the second discount = 65,280

⇒ 68000 - (x/100) × 68000 = 65280

⇒ (x/100) × 68000 = 68000 - 65280

⇒ x × 680 = 2720

⇒ x = 4

Therefore, the value of the other discount is approximately 4%.

Given:

Marked price = Rs. 6600

Selling price = Rs. 4752

Concept:

The discount percentage is calculated using the formula:

Discount Percentage = (Discount / Marked Price) × 100

where, Discount = Marked Price - Selling Price

Calculation:

We have,

⇒ Marked Price = Rs. 6600

⇒ Selling Price = Rs. 4752

⇒ Discount = Marked Price - Selling Price

⇒ Discount = 6600 - 4752

⇒ Discount = 1848

⇒ Discount Percentage = (Discount / Marked Price) × 100

⇒ Discount Percentage = (1848 / 6600) × 100

⇒ Discount Percentage = 0.28 × 100

⇒ Discount Percentage = 28%

∴ The correct answer is option 4.

Given:

Time taken by boat to cover 20 km upstream and 60 km downstream = 5 hrs.

Time taken by boat to cover 60 km upstream and 80 km downstream = 7 hrs.

Concept Used:

If 'b' is the speed of a boat and 's' is the speed of a stream then,

Upstream speed of boat = b - s

& Downstream speed of boat = b + s

Calculation:

Let the speed of the boat be 'b' and the speed of the stream be 's'.

According to the question,

{20/(b - s)} + {60/(b + s)} = 5      ----(i)

{30/(b - s)} + {80/(b + s)} = 7      ----(ii)

Let us put 1/(b - s) = P and 1/(b + s) = Q in equation (i) and (ii),

So, 

20P + 60Q = 5      ----(iii)

30P + 80Q = 7      ----(iv)

Multiplying equation (iii) by 3 and equation (iv) by 2, we get

60P + 180Q = 15      ----(v)

60P + 160Q = 14      ----(vi)

Solving these we get,

(180 - 160)Q = 15 - 14

⇒ 20Q = 1

⇒ Q = 1/20

So, P = {5 - 60 × (1/20)}/20      ----{From equation (iii)}

⇒ P = {5 - (60/20)}/20

⇒ P = (5 - 3)/20

⇒ P = 2/20

⇒ P = 1/10

So, b - s = 10 & b + s = 20

So, b = 15 km/hr and s = 5 km/hr.

∴ The speed of the boat in still water is 15 km/hr.

Given:

Simple Interest (SI) = ₹2275

Rate (R) = 13% per annum

Time (T) = 5 years

Formula used:

SI = \(\dfrac{P \times R \times T}{100}\)

Where, P = Principal

Calculation:

2275 = \(\dfrac{P \times 13 \times 5}{100}\)

⇒ 2275 = \(\dfrac{65P}{100}\)

⇒ 2275 = 0.65P

⇒ P = \(\dfrac{2275}{0.65}\)

⇒ P = 3500

∴ The correct answer is 3500.

Given:

The ratio of first and second number = 5 ∶ 2 = 25 ∶ 10

Ratio of second and third number = 5 ∶ 4 = 10 ∶ 8

Product of 1^st and 3^rd no. = 1800

Calculation:

Ratio of three number = 25 ∶ 10 ∶ 8

Let three numbers be 25a, 10a and 8a

Product of first and third number = (25a) × (8a) = 200a²

According to the question,

⇒ 1800 = 200a²

⇒ a² = 9

⇒ a = 3

Now,

∴ Sum of all numbers = 25a + 10a + 8a = 43a = 43 × 3 = 129

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Since Expenditure = 2/3 of Income, the Ratio of Expenditure to Savings = 2 : 1.

Total Income ratio = 2 + 1 = 3.

Using the weighted average method for percentage changes (Income = Exp + Sav):

3 × 18% = 2 × 24% + 1 × x%

54% = 48% + x% ⇒ x = 6%

∴ The correct answer is 6%.

Alternate Method

Given:

Expenditure = 2/3 of Income

Income increases by 18% and Expenditure increases by 24%.

Calculations:

⇒ Let the initial income be 300 units.

⇒ Initial Expenditure = (2 ÷ 3) × 300 = 200 units

⇒ Initial Savings = 300 − 200 = 100 units

⇒ New Income = 300 + (18% of 300) = 300 + 54 = 354 units

⇒ New Expenditure = 200 + (24% of 200) = 200 + 48 = 248 units

⇒ New Savings = New Income − New Expenditure

⇒ New Savings = 354 − 248 = 106 units

⇒ Increase in Savings = 106 − 100 = 6 units

⇒ Percentage Increase = (Increase ÷ Initial Savings) × 100%

⇒ Percentage Increase = (6 ÷ 100) × 100% = 6%

∴ The correct answer is 6%.

Additional Information

Income, Expenditure & Savings Relation

Income = Expenditure + Savings. The percentage change in total income is always equal to the weighted average of the percentage changes in expenditure and savings.

Percentage Change Formula

Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100. A positive result indicates an increase, while a negative result indicates a decrease.

Base Value Concept

When calculating percentage increase or decrease, the original or initial value is always taken as the base value (100%).

Given:

Marks scored by A in Hindi = 86

Marks scored by B in English = 74

Marks scored by C in English = 70

Marks scored by D in Science = 70

Calculation:

The sum of the marks scored by A in Hindi and B in English = 86 + 74 = 160

The sum of the marks scored by C in English and D in Science = 70 + 70 = 140

The required ratio = 160/140 = 8/7

∴ The correct answer is 8:7.

GIVEN:

Speed of the train = 36 km/h

Length of the train = 200 m

Train crosses a platform in 45 seconds

FORMULA USED:

Speed = Distance / Time 

CALCULATION:

Let the length of platform be ‘x’

⇒ Total distance travelled by train = x + 200

Speed of train = 36km/hr = 10 m/s

Time taken = 45 s

10 = (x + 200)/45

⇒ x + 200 = 450

∴ x = 450 - 200 = 250 m

The arrangement of the given words in the order in which they appear in an English dictionary is as shown below :

6. Diagram
7. Dialect
8. Dialogue
9. Diameter
10. Diamond
11. Dictator

Hence, the correct answer is "6, 4, 2, 5, 1, 3".