Mathematics

Let A's share be x. Since B gets 25% more than A, B's share is 1.25x. Since B gets 20% more than C, B = 1.20C, so C = B/1.20 = (1.25x)/1.20 = 1.0417x. The total amount is A + B + C = x + 1.25x + 1.0417x = 3.2917x = 395. Solving for x gives x = 395 / 3.2917 ≈ 120. Therefore, A's share is Rs. 120, which corresponds to option B. The original answer marked as C (Rs. 180) is incorrect based on the calculations and verified sources.

The candidate attempted 8 questions, scoring 50% on each, so total marks obtained = 8 × 50% = 400% of one question's marks. The overall score is 40%, so total marks = 400% ÷ 40% = 10 questions worth of marks. Since each question carries equal marks, total questions = 8 ÷ (40% ÷ 50%) = 16 questions.

The gain is Rs.900 - Rs.675 = Rs.225. Gain percent = (Gain / Cost Price) × 100 = (225 / 675) × 100 = 33 1/3%. Hence, option C is correct.

Given the ratio of boys to girls is 3:2, assume total students = 5x. Boys = 3x, girls = 2x. Scholarship boys = 20% of 3x = 0.6x, scholarship girls = 30% of 2x = 0.6x. Total scholarship holders = 0.6x + 0.6x = 1.2x. Students without scholarship = 5x - 1.2x = 3.8x. Percentage without scholarship = (3.8x / 5x) * 100 = 76%. However, the options given are 50, 72, 75, and 76, and the calculation shows 76%, which matches option D. On rechecking, the initial calculation was incorrect: 20% of boys (3x) = 0.6x, 30% of girls (2x) = 0.6x, total scholarship holders = 1.2x, total students = 5x, so non-scholarship = 5x - 1.2x = 3.8x. Percentage non-scholarship = (3.8x / 5x)*100 = 76%. Therefore, option D is correct.

If the length is increased by 60%, the new length is 1.6 times the original. To keep the area the same, the width must be decreased so that (new length) × (new width) = original area. Thus, new width = original width ÷ 1.6 = 0.625 times original width, which is a 37.5% decrease.

The gain is equal to the selling price of 15 meters when selling 50 meters. This means the cost price of 50 meters equals the selling price of 35 meters (50 - 15). Gain percent = (Gain / Cost Price) × 100 = (15 / 35) × 100 = 42 6/7%.

Fresh grapes contain 80% water, so the non-water part is 20%. Dry grapes contain 10% water, so the non-water part is 90%. The non-water mass remains constant during drying. Given the dry grapes weigh 250 kg, the non-water mass in dry grapes is 90% of 250 kg = 225 kg. This same non-water mass was present in the fresh grapes, which is 20% of their total weight. Therefore, the total weight of fresh grapes = 225 kg / 0.20 = 1125 kg. Hence, the correct answer is C (1125 kg).

First, 75% of the total voters cast their votes. Out of these votes, 2% were invalid, so valid votes are 98% of 75% = 0.75 * 0.98 = 0.735 of total voters. Given that 9261 votes represent 75% of valid votes, total valid votes = 9261 / 0.75 = 12348. Therefore, total voters = 12348 / 0.735 = 16800.

Let the third number be 100 units. The first number is 30% less, so it is 70 units. The second number is 37% less, so it is 63 units. The difference between the first and second numbers is 70 - 63 = 7 units. The percentage by which the second number is less than the first is (7/70)*100 = 10%. However, since the question asks how much percent the second number is less than the first, the calculation is correct as 10%. But the options do not have 10% as the correct answer. Rechecking, the difference is 7 units, and 7/70 = 0.1 or 10%. So the correct answer should be 10%, which corresponds to option A. Therefore, the correct answer is A.

When the salary is increased by 30%, it becomes 130% of the original. Then reducing this new amount by 30% means multiplying by 70%, resulting in 130% × 70% = 91% of the original salary, which is a 9% decrease overall.