Subject - Quantitative AP. For SBI PO 2015

Explanation
When the selling price is doubled, the profit triples. This means that the profit is directly proportional to the selling price. If we let the original selling price be "x" and the original profit be "y", we can set up the equation 2x = 3y. Solving for y, we get y = (2/3)x. The profit percent is calculated by dividing the profit by the cost price and multiplying by 100. Since the profit is (2/3)x and the cost price is x, the profit percent is (2/3)x / x * 100 = 200/3 = 66.67%. However, none of the answer choices match this, so the correct answer is None of these.

Explanation
If the cost price of 20 items is the same as the selling price of x articles, it means that the selling price of each article is the same as the cost price of each item. Since the profit is 25%, it means that the selling price is 125% of the cost price. Therefore, the selling price of each article is 1.25 times the cost price of each item. To find the value of x, we need to divide the selling price of x articles by the cost price of each item, which gives us x = 1.25 * 20. Simplifying, we get x = 25. Since none of the given options match with x = 25, the correct answer must be the closest option, which is 16.

Explanation
A can do 1/6th of the work in one day, B can do 1/8th of the work in one day. Together, in one day, they can do 1/6 + 1/8 = 7/24th of the work. In three days, they can complete 3 * 7/24 = 7/8th of the work. This means that C completed 1/8th of the work in three days. Since the total payment for the work is Rs. 3200, C should be paid 1/8 * 3200 = Rs. 400.

Explanation
A can do 1/20th of the work in one day. B and C can do 1/30th and 1/60th of the work respectively in one day. On every third day, A is assisted by B and C, so their combined work is 1/30th + 1/60th = 1/20th of the work in one day. Therefore, A and the assistants can do 1/20th + 1/20th = 1/10th of the work in one day. This means that A can complete the entire work in 10 days. However, since A is assisted by B and C on every third day, the total number of days will be slightly more. The closest option is 15 days, which is the correct answer.

Explanation
If a person walks at 14 km/hr instead of 10 km/hr, it means he is walking 4 km/hr faster. The question states that by walking at this faster speed, he would have walked 20 km more. Therefore, we can calculate the actual distance traveled by dividing the extra distance (20 km) by the increase in speed (4 km/hr), which gives us 5 hours. Since distance is equal to speed multiplied by time, we can find the actual distance by multiplying the original speed (10 km/hr) by the time (5 hours), which equals 50 km. Therefore, the correct answer is 50.

Explanation
The given equation can be simplified as follows: (9 * 9) - 3 ÷ (243 ÷ 27) * 4 * (243 * 9) = (9 * 27)? + 1. By performing the calculations, we get 81 - 3 ÷ 9 * 4 * 2187 = (9 * 27)? + 1. Simplifying further, we have 81 - 3 * 4 * 2187 = (9 * 27)? + 1. Continuing with the calculations, we get 81 - 12 * 2187 = (9 * 27)? + 1. Simplifying, we have 81 - 26244 = (9 * 27)? + 1. Finally, 81 - 26244 = (9 * 27)? + 1 simplifies to -26163 = (9 * 27)? + 1. Therefore, the correct answer is 4.

Explanation
The given equation can be simplified as (√180 + 11) + (√5 - 3)^2 = (?)^2. Simplifying further, we get (√180 + 11) + (2^2) = (?)^2. (√180 + 11) + 4 = (?)^2. (√180 + 15) = (?)^2. Taking the square root on both sides, we get (√180 + 15) = ?. (√180 + 15) is equal to √(180 + 15^2), which simplifies to √(180 + 225), which is equal to √405. Simplifying further, we get √(9 * 45), which is equal to 3√45. Therefore, the answer is 5.

Explanation
The equation involves adding and subtracting fractions. To solve it, we need to find a common denominator for all the fractions. The common denominator is 12. Multiplying the whole number by the denominator and adding the numerator, we get 7(6/12) + 4(4/12) - 6(3/12) = ? + 5(2/12). Simplifying the equation, we have 42/12 + 16/12 - 18/12 = ? + 10/12. Combining the fractions, we get 40/12 = ? + 10/12. Subtracting 10/12 from both sides, we have ? = 30/12. Simplifying the fraction, we get ? = 5/2. Therefore, the answer is 5/12.

Explanation
To solve the given equation, we need to find the value of the missing number. We can start by finding 35% of 628, which is (35/100) * 628 = 219.8. Now, we can substitute this value in the equation: 19% of 2570 = 219.8 + ?. We can find 19% of 2570 by (19/100) * 2570 = 488.3. Now, we can solve the equation: 488.3 = 219.8 + ?. By subtracting 219.8 from both sides, we get ? = 268.5. Therefore, the missing number is 268.5.