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Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm2 in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard remained a square. How many tomatoes did Anil produce this year?
- a)4225
- b)4096
- c)4356
- d)Insufficient Data
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Anil grows tomatoes in his backyard which is in the shape of a square....
Let the area of backyard be x2 this year and y2 last year
∴ X2- Y2 = 131
=) (X+Y) (X-Y) = 131
Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.
=) (X+Y) (X-Y) = 131 x 1
=) X+Y = 131
X-Y = 1
=) 2X = 132 =) X = 66
and Y = 65
∴ Number of tomatoes produced this year = 662 = 4356
Choice (C) is therefore, the correct answer.
Correct Answer: 4356
∴ X2- Y2 = 131
=) (X+Y) (X-Y) = 131
Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.
=) (X+Y) (X-Y) = 131 x 1
=) X+Y = 131
X-Y = 1
=) 2X = 132 =) X = 66
and Y = 65
∴ Number of tomatoes produced this year = 662 = 4356
Choice (C) is therefore, the correct answer.
Correct Answer: 4356
Most Upvoted Answer
Anil grows tomatoes in his backyard which is in the shape of a square....
Given:
- Each tomato takes 1 cm2 in his backyard.
- This year, he has been able to grow 131 more tomatoes than last year.
- The shape of the backyard remained a square.
To Find: How many tomatoes did Anil produce this year?
Approach:
- Let the side of the square be x cm.
- Then, the area of the square backyard will be x*x = x^2 cm^2.
- As each tomato takes 1 cm^2, the number of tomatoes that can be grown in the square backyard will be x^2.
- Let the number of tomatoes grown last year be y.
- Then, the number of tomatoes grown this year will be y+131.
- We need to find y+131.
Calculation:
- We know that the shape of the backyard remained a square.
- Therefore, the number of tomatoes grown last year can be calculated as the maximum number of tomatoes that can be grown in a square whose area is less than or equal to the area of the backyard.
- From the given options, we can calculate the area of each square and check which one is less than or equal to the area of the backyard.
- We get that the area of the square with option C is 4356 cm^2 which is greater than the area of the backyard.
- The area of the square with option B is 4096 cm^2 which is less than the area of the backyard.
- Therefore, we can conclude that the number of tomatoes grown last year is equal to the maximum number of tomatoes that can be grown in a square with an area of 4096 cm^2 which is equal to 4096.
- Hence, the number of tomatoes grown this year is y+131 = 4096+131 = 4227.
Therefore, the correct option is (a) 4225.
- Each tomato takes 1 cm2 in his backyard.
- This year, he has been able to grow 131 more tomatoes than last year.
- The shape of the backyard remained a square.
To Find: How many tomatoes did Anil produce this year?
Approach:
- Let the side of the square be x cm.
- Then, the area of the square backyard will be x*x = x^2 cm^2.
- As each tomato takes 1 cm^2, the number of tomatoes that can be grown in the square backyard will be x^2.
- Let the number of tomatoes grown last year be y.
- Then, the number of tomatoes grown this year will be y+131.
- We need to find y+131.
Calculation:
- We know that the shape of the backyard remained a square.
- Therefore, the number of tomatoes grown last year can be calculated as the maximum number of tomatoes that can be grown in a square whose area is less than or equal to the area of the backyard.
- From the given options, we can calculate the area of each square and check which one is less than or equal to the area of the backyard.
- We get that the area of the square with option C is 4356 cm^2 which is greater than the area of the backyard.
- The area of the square with option B is 4096 cm^2 which is less than the area of the backyard.
- Therefore, we can conclude that the number of tomatoes grown last year is equal to the maximum number of tomatoes that can be grown in a square with an area of 4096 cm^2 which is equal to 4096.
- Hence, the number of tomatoes grown this year is y+131 = 4096+131 = 4227.
Therefore, the correct option is (a) 4225.
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