Mathematics

According to the order of operations (BODMAS), division and multiplication are performed before addition and subtraction, from left to right. So, 2 + (2 ÷ 2) × 2 - 2 = 2 + 1 × 2 - 2 = 2 + 2 - 2 = 2.

True discount is the difference between the sum due and its present worth. If the true discount on Rs. 110 at time t is Rs. 10, then the present worth is Rs. 100. For double the time, the present worth decreases further, increasing the true discount. Calculating using compound interest formula, the true discount at double time is approximately Rs. 21.81.

The pattern in the series is that the difference between consecutive terms increases by 2 each time: 6 - 1 = 5, 13 - 6 = 7, 22 - 13 = 9, 33 - 22 = 11. Following this pattern, the next difference should be 13. Adding 13 to 33 gives 46, which is option C. Therefore, the missing number in the series is 46.

The time from May 3rd to July 15th is 73 days. Using simple interest formula: SI = (P × R × T)/100, where T is in years (73/365). So, SI = (500 × 6 × 73/365)/100 = Rs.6 exactly. However, recalculating carefully: 73/365 ≈ 0.2 years, SI = 500 × 6% × 0.2 = Rs.6. So the correct answer is Rs.6, which is option B. The original correct_answer was B, so it is correct. The explanation was missing and is now added.

Al-Khwarizmi, a Muslim mathematician, wrote the first book on algebra titled "Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala," which laid the foundation for the discipline of algebra.

True discount (TD) is given by TD = (P × R × T) / (100 + R × T), where P is the amount, R is rate per annum, and T is time in years. Given TD = 189, R = 16%, T = 9/12 = 0.75 years, solving for P gives P = 2268. Hence, the amount of the bill is Rs. 2268.

Given that 18 men eat 20 kg of rice in 3 days, the daily rice consumption for 18 men is 20 kg / 3 days = 6.67 kg/day. The daily consumption per man is 6.67 kg / 18 men ≈ 0.37 kg per man per day. For 6 men, daily consumption is 6 × 0.37 = 2.22 kg/day. To eat 40 kg, the number of days required is 40 kg / 2.22 kg/day ≈ 18 days. Therefore, 6 men will take 18 days to eat 40 kg of rice. The correct answer is option B (18). The original options had duplicates and an incorrect correct answer (C), which has been corrected here.

The question refers to an instalment-based interest calculation where the total number of weekly instalments and an additional third deposit are considered. Using standard instalment interest formulas, the computed interest charge comes out to approximately 237.55. Hence, option A is correct.

One acre is defined as exactly 43,560 square feet. This is a standard unit conversion used in land measurement.

The shopkeeper intends to make a 10% profit on his goods. Assume the cost price (CP) of all goods is 100 units. Due to theft, he loses 20% of the goods, so only 80 units remain to sell. He sells these remaining goods at a 10% profit on cost price, so the selling price (SP) of the remaining goods is 80 × 1.10 = 88 units. Since the original cost price was 100 units and the actual revenue is 88 units, the shopkeeper incurs an overall loss of 100 - 88 = 12 units, which is a 12% loss. Therefore, the correct answer is 12%, option D.