Explanation

Given:

Selling price (SP) = Rs. 8413

Loss percentage = 6%

Let's denote the cost price as CP.

Since the shopkeeper loses 6%, the selling price is 94% of the cost price (100% - 6% = 94%).

SP = 0.94 × CP

8413 = 0.94 × CP

CP = 8413 / 0.94

CP = 8950

Explanation

To determine significant figures in 10.03:

• All non-zero digits are significant → 1 and 3
• Zeros between non-zero digits are significant → 0 between 1 and 3
• Zeros after a decimal and a non-zero digit are also significant → the 0 after the decimal is significant

So: 1, 0, 0, 3 → 4 significant figures

Explanation

To factorize the quadratic expression 2x² + 5x + 2, we need to find two numbers whose product is 2 × 2 = 4 and whose sum is 5. These numbers are 4 and 1.

2x² + 5x + 2 = 2x² + 4x + x + 2

= 2x(x + 2) + 1(x + 2)

= (x + 2)(2x + 1)

Explanation

Explanation

Given:

105 increased in the ratio 9 : 7

To increase 105 in the ratio 9 : 7, we'll multiply 105 by 9/7:

New value = 105 × (9/7)

= 15 × 9

= 135

Explanation

• Military Overextension: Constant wars (e.g., Deccan campaigns) drained resources.
• Religious Policies: Aurangzeb’s reversal of Akbar’s tolerance alienated Hindus and Sikhs, sparking rebellions (e.g., Sikh uprisings, Rajput conflicts).
• Economic Strain: Heavy taxation and famine weakened the agrarian economy.
• Administrative Breakdown: Corruption grew, and regional governors (like the Nizam of Hyderabad) gained autonomy.

Explanation

To find the fourth proportional, let's denote it as x. The proportion will be:

3 : 9 = 7 : x

We can cross-multiply:

3x = 9 × 7

3x = 63

x = 63 / 3

x = 21

Explanation

Given:

g : h = 8 : 9

h : i = 9 : 12

To find the combined ratio g : h : i, we need to make the ratio of h the same in both.

g : h = 8 : 9

h : i = 9 : 12

Since h has the same ratio in both (9), we can directly combine:

g : h : i = 8 : 9 : 12

Explanation

Given:

Side of square = 1200 cm

Width of strip = 10 cm

Side of larger square (including strip) = 1200 + 2(10)

= 1200 + 20

= 1220 cm

Area of larger square = 1220² = 1488400 cm²

Area of square = 1200² = 1440000 cm²

Area of strip = Area of larger square - Area of square

= 1488400 - 1440000

= 48400 cm²

Explanation

Daily spending = 35 rupees, so for 7 days: 35 × 7 = 245 rupees.

Simple multiplication gives the total weekly expenditure.