Let the speed of boat in still water be u km/hr.

The speed of current = v = 2 km/hr

⇒ The downstream of boat = u + v = 17 km/hr

⇒ The speed of boat in still water = u = 17 - 2 = 15 km/hr

⇒ The upstream of boat = u - v = 15 - 2 = 13 km/hr

We know that,

Time = Distance/Speed

Given:

m ∶ n = 2 ∶ 3

x ∶ y = 4 ∶ 5

Solution:

Let m = 2a and n = 3a 

x = 4b and y = 5b

Putting the above value in the given expression, we will get:

⇒ 10mx + 4ny ∶ 5mx + 3ny 

⇒ (10 × 2a × 4b) + (4 × 3a × 5b) ∶ (5 × 2a × 4b)  +  (3 × 3a × 5b)

⇒ (80ab) + (60ab) : (40ab) + (45ab)

⇒ 140ab : 85ab = 28 : 17

Given:

Formula Used:

From the tangent theorem,

PT² = PA x PB

Calculations:

⇒ Here, PT = 12 cm

⇒ PB = 24 cm

Now put the value of PT and PB 

⇒ PT² = PA x PB

⇒ 12² = PA x 24

⇒ PA = 144 / 24 = 6 cm

As we know,

⇒ PB = PA + AB

⇒ AB = PB - PA = 24 - 6 = 18 cm

⇒ Hence, The value of AB is 18 cm.

Total time taken by Gorang for doing work

= Monday + Tuesday + Wednesday + Friday

Short trick:

Cost price = 5600 × 83/100 - 500 = Rs. 4148

Detailed solution:

Marked price of TV set = Rs. 5600

Discount = 17%

Selling Price of TV set after discount,

= 5600 - 5600 × (17/100)

= 5600 - 56 × 17

= 5600 - 952

= 4648

Selling price of TV set = Rs. 4648

Profit earned (given) = Rs. 500

Profit = S.P - C.P

⇒ 500 = 4648 - C.P

⇒ C.P = 4148

∴ Cost price of TV set is Rs. 4148.

Thus, the correct answer is option 2.

Given:

A cuboid having length 6 cm, breadth 7 cm and height 8 cm

Concept used: 

Surface area = 2(LB + BH + HL)

Calculation:

⇒ Surface area = 2[(6 x 7) + (7 x 8) + (8 x 6)]

⇒ 2(42 + 56 + 48)

⇒ 2 x 146

⇒ 292 cm²

∴ The surface area of a cuboid having length 6 cm, breadth 7 cm and height 8 cm is 292 cm²

Given:

Amount of money taken on Loan by Jay = Rs 10,000.

Rate of interest = 5%

Time = 2 years.

Concept:

Simple interest = ((P × R × T)/100)

Equivalent Rate on Compound interest = ( X + Y + ((X × Y)/100) 

Calculation:

Equivalent Rate on Compound interest = ( 5 + 5 + ((5 × 5)/100) = 10.25%

Total simple interest on Rs 10000 at 5% for 2 years = (10,000 × 10%) = Rs 1000

Total Compound interest on Rs 10000 at 5% for 2 years = (10,000 × 10.25%) = Rs 1025

Difference in the Interest paid = Rs 25

GIVEN:

A received Rs. 24000

B received Rs. 35000

C received Rs. 57000

FORMULA:

Profit Share ratio = Investment Amount × Investment Time

CALCULATION:

Let the ratio of money investment be x : y : z

⇒ Ratio of profit share = 2x : 5y : 3z

According to the question

2x : 5y : 3z = 24000 : 35000 : 57000 = 24 : 35 : 57

⇒ x : y : z = 12 : 7 : 19

Given:

The ratio of the radius of the two circles = 2 : 3

Formula used:

The circumference of the circle = 2 × π × r      (Where, r = The radius of the circle)

Calculation:

Let be assume the radius of the circles is 2p and 3p respectively

⇒ The circumference of the first circle = 2 × π × (2p)

⇒ The circumference of the second circle = 2 × π × (3p)

⇒ The required ratio of the circumferences = { 2 × π × (2p)}/{2 × π × (3p)} = 2 : 3

∴ The required result will be 2 : 3.