Explanation

- Let total shares = T

- Company S owns 30% of T = 0.30T

- Company T owns 12,000 shares

- Company R owns the remaining shares: T - (S + T) = T - (0.30T + 12,000) = 0.70T - 12,000

- Given Company R has 15% more shares than Company S:  

  R = S + 15% of S = 1.15 × S

So,

0.70T - 12,000 = 1.15 × 0.30T  

0.70T - 12,000 = 0.345T  

0.70T - 0.345T = 12,000  

0.355T = 12,000  

T = 12,000 / 0.355 ≈ 33,802.82 shares (total shares)

Now, Company S owns:  

S = 0.30 × 33,802.82 ≈ 10,140 shares

Explanation

- 3 pointers point 3 walls in 3 minutes.

- So, 1 pointer points 1 wall in 3 minutes.

Now, we want to know how many pointers are needed to point 27 walls in 9 minutes.

Since 1 pointer points 1 wall in 3 minutes, in 9 minutes (which is 3 times longer), 1 pointer can point:

1 wall × 3 = 3 walls.

To point 27 walls in 9 minutes:

Number of pointers needed = Total walls / Walls per pointer = 27 / 3 = 9 pointers.

Explanation

In a proportion, cross-multiply:  

4 × 16 = 8 × x  

64 = 8x  

Divide both sides by 8:  

x = 64 / 8  

x = 8

Explanation

Original price = Rs. 400  

Discount = 25% of Rs. 400 = (25/100) × 400 = Rs. 100  

Sale price = Original price - Discount = 400 - 100 = Rs. 300  

Explanation

He sells 40% of them, so he is left with 60% of x. According to the problem: 60% of x = 360 => (60/100) * x = 360 => 0.6x = 360 => x = 360 / 0.6 => x = 600

He sells 40% of them, so he is left with 60% of x.

According to the problem:

60% of x = 360  

=> (60/100) * x = 360  

=> 0.6x = 360  

=> x = 360 / 0.6  

=> x = 600

According to the problem:

60% of x = 360  

=> (60/100) * x = 360  

=> 0.6x = 360  

=> x = 360 / 0.6  

=> x = 600

Explanation

Given:

- Principal (P) = Rs. 42,000

- Annual interest rate (r) = 6% = 0.06

- Time (t) = 10 years

- Interest compounded half-yearly (n = 2 times per year)

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Formula for compound interest:

Amount, A = P * (1 + r/n)^(n*t)

Substitute the values:

A = 42,000 * (1 + 0.06/2)^(2 * 10)  

= 42,000 * (1 + 0.03)^20  

= 42,000 * (1.03)^20

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Calculate (1.03)^20:

(1.03)^20 ≈ 1.8061

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So,

A ≈ 42,000 * 1.8061 ≈ Rs. 75,856.2

Explanation

a² − b² = 9  

But we can also write:

a² − b² = (a + b)(a − b) = 9  

And  

(a − b)² = 3 → so (a − b) = √3 or −√3

Let’s assume:  

a − b = √3

Then:  

From (a + b)(a − b) = 9  

⇒ (a + b)(√3) = 9  

⇒ a + b = 9 / √3 = 3√3

Now, we have:  

a + b = 3√3  

a − b = √3

Now solve the system:

Adding:  

2a = 4√3 → a = 2√3  

Subtracting:  

2b = 2√3 → b = √3

Now, ab = a × b = 2√3 × √3 = 2 × 3 = 6

Explanation

Given:  

x = 5, y = 2

Expression:  

2x + 3y = 2(5) + 3(2) = 10 + 6 = 16

Explanation

Cow 1 (4000 l) increases by 15%:  

15% of 4000 = 0.15 × 4000 = 600  

New amount = 4000 + 600 = 4600 l

Cow 2 (3100 l) increases by 10%:  

10% of 3100 = 0.10 × 3100 = 310  

New amount = 3100 + 310 = 3410 l

Total production in 2nd year = 4600 + 3410 = 8010 l

Explanation

Odd numbers in the list:  

3, 7, 37, 41

Sum = 3 + 7 + 37 + 41 = 88

88 is an even number.