Indian Mathematical Puzzles and Riddles

To find the total number of animals, we simply add the number of sheep, cows, and pigs: 12 + 6 + 8 = 30.

To find the time at which the two trains meet, we need to calculate the relative speed between them. The relative speed is the difference between the speeds of the two trains: 70 - 60 = 10 miles per hour. Then, we divide the distance between Mumbai and Delhi by the relative speed: 800 / 10 = 80 hours. Since the second train leaves at 11:00 AM, we add 80 hours to this time to find the time at which the two trains meet: 11:00 AM + 80 hours = 3:00 PM.

Let the cost price of the shirt be (x). Then, the profit made by the shopkeeper is (20)% of (x), which is (0.2x). The selling price of the shirt is the cost price plus the profit, which is (x + 0.2x = 1.2x). We know that the selling price is ($20), so we can set up the equation (1.2x = 20) and solve for (x). (x = 20 / 1.2 = $16).

The area of a rectangle is calculated by multiplying its length and width. Therefore, the area of the field is (20 \times 15 = 300) square meters.

First, we need to convert the speed of the train from kilometers per hour to meters per second. (72) kilometers per hour is equal to (72 \times 1000 / 60 / 60 = 20) meters per second. Then, we can use the formula (distance = speed \times time) to find the length of the train. The distance traveled by the train in (30) seconds is (20 \times 30 = 600) meters. Therefore, the length of the train is (600) meters.

The shopkeeper sells (40)% of the apples at a profit of (20)%. This means he sells (0.4 \times 100 = 40) apples at a profit of (20)% each. The profit on each apple is (0.2 \times $1) = $0.2). Therefore, the total profit on (40) apples is (40 \times $0.2) = $8). The shopkeeper sells the remaining (60)% of the apples at a loss of (10)%. This means he sells (0.6 \times 100 = 60) apples at a loss of (10)% each. The loss on each apple is (0.1 \times $1) = $0.1). Therefore, the total loss on (60) apples is (60 \times $0.1) = $6). The overall profit or loss is the difference between the total profit and the total loss, which is ($8) - ($6) = ($2). Therefore, the shopkeeper makes an overall profit of ($2).

Since roosters do not lay eggs, only the hens lay eggs. There are (12) hens, and each hen lays (1) egg per day. Therefore, in (7) days, each hen lays (7) eggs. The total number of eggs collected in (7) days is (12 \times 7 = 84) eggs.

To find the time at which the second train overtakes the first train, we need to calculate the relative speed between them. The relative speed is the difference between the speeds of the two trains: (70 - 60 = 10) miles per hour. Then, we need to find the distance between the two trains at (11:00) AM. The first train travels for (1) hour at a speed of (60) miles per hour, so it travels (60) miles. Therefore, the distance between the two trains at (11:00) AM is (60) miles. Now, we can divide the distance between the two trains by the relative speed to find the time it takes for the second train to overtake the first train: (60 / 10 = 6) hours. Since the second train leaves at (11:00) AM, it will overtake the first train at (11:00) AM + (6) hours = (2:00) PM.

Let the cost price of the shirt be (x). Then, the profit made by the shopkeeper is (20)% of (x), which is (0.2x). The selling price of the shirt is the cost price plus the profit, which is (x + 0.2x = 1.2x). We know that the selling price is ($25), so we can set up the equation (1.2x = 25) and solve for (x). (x = 25 / 1.2 = $21).

The farmer plants wheat on (60)% of the land, which is (0.6 \times 100 = 60) acres. He plants rice on (20)% of the land, which is (0.2 \times 100 = 20) acres. Therefore, the remaining land is (100 - 60 - 20 = 20) acres. This is the land on which the farmer plants vegetables.

To find the time at which the two trains are (300) miles apart, we need to calculate the relative speed between them. The relative speed is the sum of the speeds of the two trains: (60 + 70 = 130) miles per hour. Then, we need to find the distance between the two trains at (11:00) AM. The first train travels for (1) hour at a speed of (60) miles per hour, so it travels (60) miles. The second train travels for (1) hour at a speed of (70) miles per hour, so it travels (70) miles. Therefore, the distance between the two trains at (11:00) AM is (60 + 70 = 130) miles. Now, we can divide the distance between the two trains by the relative speed to find the time it takes for the two trains to be (300) miles apart: (300 / 130 = 2.3) hours. Since the second train leaves at (11:00) AM, the two trains will be (300) miles apart at (11:00) AM + (2.3) hours = (2:00) PM.

Let the cost price of the shirt be (x). Then, the profit made by the shopkeeper is (25)% of (x), which is (0.25x). The selling price of the shirt is the cost price plus the profit, which is (x + 0.25x = 1.25x). We know that the selling price is ($20), so we can set up the equation (1.25x = 20) and solve for (x). (x = 20 / 1.25 = $16).

To find the time at which the second train is (100) miles ahead of the first train, we need to calculate the relative speed between them. The relative speed is the difference between the speeds of the two trains: (70 - 60 = 10) miles per hour. Then, we need to find the distance between the two trains at (11:00) AM. The first train travels for (1) hour at a speed of (60) miles per hour, so it travels (60) miles. Therefore, the distance between the two trains at (11:00) AM is (60) miles. Now, we can divide the distance between the two trains by the relative speed to find the time it takes for the second train to be (100) miles ahead of the first train: (100 / 10 = 10) hours. Since the second train leaves at (11:00) AM, it will be (100) miles ahead of the first train at (11:00) AM + (10) hours = (1:00) PM.

Let the cost price of the shirt be (x). Then, the profit made by the shopkeeper is (20)% of (x), which is (0.2x). The selling price of the shirt is the cost price plus the profit, which is (x + 0.2x = 1.2x). We know that the selling price is ($24), so we can set up the equation (1.2x = 24) and solve for (x). (x = 24 / 1.2 = $20).