Tech Mahindra Palcement Papers-1

Explanation
To find the value of (7x + 4y) / (x - 2y), we need to substitute the given value of x/2y into the expression. Since x/2y = 3/2, we can replace x/2y with 3/2 in the expression. Simplifying further, we get (7(3/2) + 4y) / ((3/2) - 2y). Multiplying 7 by 3/2 gives us 21/2, so the expression becomes (21/2 + 4y) / ((3/2) - 2y). Since the question does not provide any additional information about the value of y, we cannot determine the exact value of the expression. Therefore, the answer is "data insufficient".

Explanation
The given expression can be simplified as follows:

(0.75 * 0.75 * 0.75 - 0.001) / (0.75 * 0.75 - 0.075 + 0.01)
= (0.421875 - 0.001) / (0.5625 - 0.075 + 0.01)
= 0.420875 / 0.4975
= 0.845

Therefore, the correct answer is 0.845.

Explanation
A can complete the work in 8 days, so in one day A can complete 1/8th of the work.
B can work three times faster than A, so in one day B can complete 3/8th of the work.
C can work five times faster than A, so in one day C can complete 5/8th of the work.
When they work together, the total work done in one day is (1/8 + 3/8 + 5/8) = 9/8.
Therefore, they will take (8/9) days to complete the work together.

Explanation
The distance travelled can be calculated by using the formula: Distance = Speed × Time. Let's assume the speed during the forward journey is x km/hr. Therefore, the distance travelled in the forward journey is 7x km. During the return journey, the speed increases by 12 km/hr, so the speed becomes (x + 12) km/hr. The time taken during the return journey is 5 hrs. Using the formula, the distance travelled in the return journey is (x + 12) × 5 km. Since the distance travelled in the forward and return journeys is the same, we can equate the two distances and solve for x. After solving, we find that x = 6 km/hr. Therefore, the distance travelled is 7x = 7 × 6 = 42 km. Since this distance is not one of the options, the correct answer is none of these.

Explanation
The speed of the stream can be calculated by finding the difference between the speed of the boat in still water and the speed of the boat in upstream. In this case, the boat's speed in still water is the average of its speed in upstream and downstream, which is (14 + 40)/2 = 27 km/hr. The speed of the stream is then calculated by subtracting the boat's speed in still water from its speed in upstream, which is 27 - 14 = 13 km/hr.

Explanation
If a company gives a 25% discount on an item, they are essentially selling the item for 75% of its original price. This means that they are making a profit of 25% on the cost price of the item. If they now give a 10% discount, they would be selling the item for 90% of its original price. To find the profit percentage, we need to calculate the difference between the selling price (90% of the original price) and the cost price, and then divide it by the cost price. The difference is 10%, and when divided by the cost price, it gives a profit percentage of 30%.

Explanation
The correct answer is Rs. 800. This can be calculated using the formula for simple interest: SI = P * R * T, where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period. By substituting the given values, we can find the principal amount. In this case, the principal amount is Rs. 800.

Explanation
If a sum of money compounds annually and becomes thrice itself in 3 years, it means that the interest rate is 100% per year. Therefore, the money will double every year. To become 9 times itself, it will take 3 more years, as the money will double three more times. Thus, it will take a total of 6 years for the sum of money to become 9 times itself.

Explanation
Let's assume that the original number of men is x. According to the given information, x men can finish the work in 10 days, and x-10 men will take 10 days more to finish the work. This implies that the rate at which work is done is inversely proportional to the number of men. Using the formula for inverse variation, we can write the equation (x)(10) = (x-10)(10+10). Simplifying this equation, we get 10x = 20(x-10). Solving for x, we find that x = 110. Therefore, there were originally 110 men.

Explanation
The slower train is moving at 50 kmph and the faster train is moving at 32 kmph. The slower train takes 15 seconds to completely pass the man in the slower train. This means that in 15 seconds, the slower train travels a distance equal to its own length plus the length of the faster train. Since the slower train is moving at 50 kmph, it covers a distance of (50 kmph)*(15 seconds) = 750 meters in 15 seconds. Therefore, the length of the faster train is 750 meters (or 75 meters).

Explanation
The given question asks for an expression that represents x% of y. The correct answer is x, as x% of y is equal to x/100 * y, which simplifies to x. Therefore, the expression x represents x% of y.

Explanation
If the price of sugar increases by 20%, the housewife needs to reduce her consumption by 16.66% in order to maintain the same expenditure on sugar as before. This is because a 20% increase in price would result in a 20% decrease in the quantity of sugar that can be purchased with the same amount of money. Therefore, the housewife needs to reduce her consumption by 16.66% (which is 1/6th of the original quantity) to maintain the same expenditure.

Explanation
Since each mesh is 8mm long and 5mm wide, the area of each mesh can be calculated by multiplying the length and width, which gives us 40mm². To find the number of meshes in 1 square meter, we need to convert the area from mm² to m². Since 1m = 1000mm, 1m² = (1000mm)² = 1,000,000mm². Dividing 1,000,000mm² by 40mm² gives us 25,000 meshes.

Explanation
The man spends half of his salary on household expenses, 1/4th for rent, and 1/5th for travel expenses. This means that he spends a total of (1/2 + 1/4 + 1/5) = 19/20 of his salary on these expenses. The remaining amount, which is 1 - 19/20 = 1/20 of his salary, is deposited in the bank. If this deposited amount is equal to Rs. 50, then 1/20 of his salary is equal to Rs. 50. Multiplying both sides by 20 gives us his monthly salary, which is Rs. 1000.

Explanation
If 15 men take 21 days of 8 hours each to do the work, then the total work done is 15 * 21 * 8 = 2520 man-hours.

If 3 women do as much work as 2 men, then the work done by 3 women is equivalent to the work done by 2 men.

So, the work done by 21 women is equivalent to the work done by (2/3) * 21 = 14 men.

The total work done by 21 women is 14 * x * 6, where x is the number of days of 6 hours each.

Setting this equal to 2520 man-hours, we get 14 * x * 6 = 2520.

Simplifying, we find x = 30.

Therefore, it would take 30 days of 6 hours each for 21 women to do the work.

Explanation
The diameter of a sphere is equal to the diameter of the cylinder it is made from. Since the cylinder has a diameter of 6 cms, the spheres made from it will also have a diameter of 6 cms. Therefore, the correct answer is 6 cms.

Explanation
The difference between compound interest and simple interest on a certain sum is given as Rs 25. This implies that the compound interest is higher than the simple interest. Since the difference between compound interest and simple interest increases with an increase in the principal amount, we can conclude that the sum lent out is less than Rs 15000. However, since the difference is only Rs 25, it cannot be Rs 15000. Therefore, the sum must be Rs 10000.

Explanation
In order for 2880 to be a perfect square, it must be divisible by a number that, when multiplied by itself, equals 2880. The smallest number that satisfies this condition is 5. When 2880 is divided by 5, the result is 576, which is a perfect square (24^2). Therefore, 5 is the smallest number by which 2880 must be divided to make it a perfect square.

Explanation
The father's age is currently 40 years. This can be determined by setting up an equation. Let's assume the son's current age is x. According to the given information, the father is 30 years older than the son, so the father's current age is x + 30. After 5 years, the son's age will be x + 5 and the father's age will be x + 30 + 5 = x + 35. It is also given that the father will be thrice as old as the son after 5 years. So, we can set up the equation: x + 35 = 3(x + 5). Solving this equation, we get x = 5. Therefore, the father's current age is x + 30 = 5 + 30 = 40 years.