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Given:

⇒ Speed upstream = 35/7 = 5kmph

⇒ Speed of stream = 20kmph

⇒ Speed of boat in still water = 20 + 5 = 25 kmph

⇒ Speed downstream = 25 + 20 = 45 kmph

∴ Required time = 45/45 + 20/5 = 5 hours

Given:

The difference in selling price of an article when sold at 21% profit and 10% loss is Rs. 589

Formula used:

Selling Price = Cost Price (100% ± Profit or Loss) [ + for Profit and - for loss ]

Calculation:

let cost price be 100x,

Selling Price at 21% profit = 100x (100% + 21%)

= \(100x \times \frac{121}{100}\)

= 121x

Selling Price at 10% loss = 100x (100% - 10%)

= \(100x \times \frac{90}{100}\)

= 90x

The difference in selling price of an article when sold at 21% profit and 10% loss is Rs. 589,

121x - 90x = 589

31x = 589

x = 589/31

x = 19

Cost price = 100x

= 100 × 19

= 1900

Selling Price at 25% profit = 1900 (100% + 25%)

= \(1900 \times \frac{125}{100}\)

= 19 × 125

= 2375

Selling price at 25% profit is Rs. 2375

Answer is Rs. 2375.

Alternate MethodGiven:

The difference in selling price of an article when sold at 21% profit and 10% loss is Rs. 589

Formula used:

Selling Price = Cost Price (1 ± Profit or Loss) [ + for Profit and - for loss ]

Calculation:

let 100% be cost price,

Difference in selling price,

21% - (-10%) = 589

21% + 10% = 589

31% = 589

1% = 19

Cost price = 100%

= 100 × 19

= 1900

Selling Price at 25% profit = 1900 (1 + 25%)

= \(1900 \times \frac{125}{100}\)

= 19 × 125

= 2375

Selling price at 25% profit is Rs. 2375

Answer is Rs. 2375.

Given:

Sum of money becomes 6 times of itself in 7 years

Formula used:

SI = PRT/100

Where, P = principal

R = rate

T = time

A = SI + P

Where, A = Amount

SI = simple interest

Calculation:

Let the principal be P.

For 7 years,

SI = (P × R × 7)/100

⇒ 7PR/100

A = SI + P

⇒ 6P = 7PR/100 + P

⇒ 5P = 7PR/100

⇒ R = 500/7

For 42 years,

SI = (P × R × 42)/100

⇒ {P × (500/7) × 42}/100

⇒ 30P

A = SI + P

⇒ A = 30P + P

⇒ A = 31P

∴ In 42 years, amount will become 31 times of principal.

Given:

The ratio of the present ages of A and B = 5 : 8

The ratio of the present ages of C and B = 3 : 2

The sum of their ages = 100 years

Calculation:

As per the question, the ratio of A and B is given and the ratio of C and B is given, so on equalizing the ratio of B in both ratios:

A and B = 5 : 8      ----(1)

C and B = 3 : 2      ----(2)

After multiplying 4 in equation (2), B become equal in both the equations:

A : B : C = 5 : 8 : 12

The sum of their present ages ratio = 5 + 8 + 12

⇒ 25 units

Value of 25 units = 100 years

Value of 1 unit = 4 years

So. the present age of A = 5 units

⇒ 5 × 4

⇒ 20 years

 ∴ The present age of A is 20 years.

Given:

A and B invested Rs. 8000 for 2 years and 3 years respectively

B withdrew 60% of his amount after one year of investing

Formula used:

Ratio of profit is the product of capital and time

Calculation:

Effective investment of A

⇒ 8000 × 2 = Rs. 16000

Effective investment of B

⇒ 8000 × 1 + (40/100) × 8000 × 2 = 8000 + 6400 = 14400

∴ Ratio of their profits = 16000 : 14400 = 10 : 9

Given:

13860, 6930, ?, 462, 66, 6

Calculation:

The Series follows the following pattern

13860 ÷ 2 = 6930

6930 ÷ 3 = 2310

2310 ÷ 5 = 462

462 ÷ 7 = 66

66 ÷ 11 = 6

∴ The Required term in the series will be 2310

Note: this series divide by a prime number like 2, 3, 5, 7, 11

Calculation:

The series follows following pattern:

⇒ 7

⇒ 7 + (2)² = 11

⇒ 11 + (3)² = 20

⇒ 20 + (4)² = 36

⇒ 36 + (5)² = 61

⇒ 61 + (6)² = 97

∴ The missing number in place of ‘?’ is 20.

Given:

The number series:

900, 890, 870, 830, 750, ?

Concept Used:

Number series following a fixed pattern.

Calculation;

The given number series follows the pattern:

900 – (10 × 2⁰) = 890

890 – (10 × 2¹) = 870

870 – (10 × 2²) = 830

830 – (10 × 2³) = 750

750 – (10 × 2⁴) = 590

∴ The Missing Number in the given number series is 590

This series follows following pattern:

⇒ 171 + 2 = 173

⇒ 173 – 3 = 170

⇒ 170 + 5 = 175

⇒ 175 – 7 = 168

⇒ 168 + 11 = 179

∴ The value of ? is 168

The given series follows the given pattern,

1³ + 1 = 2

2³ + 2 = 10

3³ + 3 = 30

4³ + 4 = 68

5³ + 5 =130

6³ + 6 = 222       

∴ The missing term in the series is 30.