To answer this question, let's calculate the hourly wages of Y and determine how much Y will receive for the same work.

Given that X is 25% more efficient than Y, we can say that if Y takes 100 units of time to complete a task, then X will take 75 units of time.

Now, let's consider the hourly wages. It is given that X's hourly wages are 25% more than Y's. So, if Y is paid Rs. 100 for 100 units of time, X will be paid Rs. 125 for 75 units of time.

To find out how much Y will receive for the same work, we need to calculate the amount paid per unit of time for Y.

Y's hourly wage = X's hourly wage * (100 units of time / 75 units of time)

Y's hourly wage = Rs. 125 * (100/75)

Y's hourly wage = Rs. 100

Therefore, Y will receive Rs. 100 for the same work.

The correct answer is C) 75.

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To solve this problem, we need to calculate the ratio of the investments made by P, Q, and R initially.

Let's calculate the ratio of their investments:

P's investment = Rs. 20000 Q's investment = Rs. 30000 R's investment = Rs. 40000

To calculate the ratio, we divide each investment by the total investment:

Total investment = Rs. (20000 + 30000 + 40000) = Rs. 90000

P's ratio = Rs. 20000 / Rs. 90000 = 2/9 Q's ratio = Rs. 30000 / Rs. 90000 = 3/9 = 1/3 R's ratio = Rs. 40000 / Rs. 90000 = 4/9

Now, let's calculate the time for which each partner remains in the partnership:

P remains in the partnership for 2 months. Q remains in the partnership for 4 months. R remains in the partnership for 8 months.

To calculate the share of each partner, we multiply their ratios with their respective time periods:

P's share = (2/9) * 2 = 4/9 Q's share = (1/3) * 4 = 4/9 R's share = (4/9) * 8 = 32/9

Now, let's calculate the total share of R:

Total share of R = R's share / (P's share + Q's share + R's share) * Total Profit

Total share of R = (32/9) / (4/9 + 4/9 + 32/9) * Rs. 12474

Total share of R = (32/9) / (40/9) * Rs. 12474

Total share of R = (8/40) * Rs. 12474

Total share of R = (1/5) * Rs. 12474

Total share of R = Rs. 2494.8

Therefore, R's share in the profit of Rs. 12474 is approximately Rs. 2494.8.

Since none of the given options match this value exactly, there might be a mistake in the question or the answer choices provided.

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To solve this problem, let's break it down into steps:

Step 1: Calculate the initial income from selling the shares at Rs.20 each. The initial investment is 250 shares at Rs.10 each, so the total investment is 250 * 10 = Rs.2500. When these shares are sold at Rs.20 each, the total income is 250 * 20 = Rs.5000.

Step 2: Calculate the income after receiving a dividend of 10%. The dividend received is 10% of the initial income, which is 10% of Rs.5000 = Rs.500. The total income after receiving the dividend is Rs.5000 + Rs.500 = Rs.5500.

Step 3: Calculate the income after investing the dividend in another company. The dividend of Rs.500 is used to buy shares in another company at Rs.4 each. So, the number of shares bought is Rs.500 / Rs.4 = 125 shares.

Step 4: Calculate the income from the new investment. The new investment is 125 shares at Rs.5 each, so the total investment is 125 * 5 = Rs.625. The income from selling these shares at Rs.20 each is 125 * 20 = Rs.2500.

Step 5: Calculate the income after receiving a dividend of 4% on the new investment. The dividend received is 4% of the income from the new investment, which is 4% of Rs.2500 = Rs.100. The total income after receiving the dividend is Rs.2500 + Rs.100 = Rs.2600.

Step 6: Calculate the difference in income. The initial income was Rs.5500, and the income after the new investment is Rs.2600. The difference in income is Rs.5500 - Rs.2600 = Rs.2900.

Therefore, the difference in income is Rs.2900.

Since the correct answer is not among the given options (A, B, C, or D), it seems that there might be an error in the options provided. Please double-check the options or consult the original source for the correct answer.

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To solve this question, let's analyze the transactions step by step:

1. X buys an apple from Y for Rs.5. X's initial cost is Rs.5.
2. X sells the apple to Z for Rs.10. X's profit from this transaction is Rs.10 - Rs.5 = Rs.5.
3. X buys the apple back from Z for Rs.12. X's total cost is now Rs.5 + Rs.12 = Rs.17.
4. X sells the apple to Y for Rs.15. X's profit from this transaction is Rs.15 - Rs.17 = -Rs.2.

So, overall, X has a loss of Rs.2 over the venture.

Therefore, the correct answer is not given among the options. None of the options A, B, C, or D is correct.

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To solve this problem, we can use the concept of the tangent to a circle.

Let's assume that the centers of the three circles are O₁, O₂, and O₃, and their radii are r₁, r₂, and r₃, respectively.

Given that the circles touch each other externally, the tangents drawn at the points of contact will pass through the centers of the circles. Therefore, the line joining the centers of two tangent circles will form a right triangle with the radii as the hypotenuse.

Using this concept, we can solve the problem using the given information.

From the given information, we have: xy = 15 yz = 10 xz = 21

Let's consider the right triangle formed by O₁, O₂, and the point of contact.

In this triangle, the hypotenuse is r₁ + r₂, and the legs are r₁ and r₂.

Using the Pythagorean theorem, we can write the equation as: (r₁ + r₂)² = r₁² + r₂²

Expanding the equation, we get: r₁² + 2r₁r₂ + r₂² = r₁² + r₂²

Simplifying, we get: 2r₁r₂ = 0

Since r₁ and r₂ are both positive, this implies that r₁ = 0, which is not possible.

Therefore, the only possible solution is that r₁ = 0, and r₂ + r₃ = xz = 21.

From xy = 15, we can find that r₂ = 15/y = 15/3 = 5.

Substituting r₂ = 5 into r₂ + r₃ = 21, we get: 5 + r₃ = 21 r₃ = 21 - 5 r₃ = 16

Hence, the radii of the three circles are r₁ = 0, r₂ = 5, and r₃ = 16.

Therefore, the correct answer is option A) 0, 5, 16.

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