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Mr. Baker runs a bakery shop. One day he made some cakes of different weights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?
Correct answer is '3'. Can you explain this answer?
Verified Answer
Mr. Baker runs a bakery shop. One day he made some cakes of differentw...
Ans.
Method to Solve :
100 kg total weight.
Heaviest two – 12.5 kg average
, lightest 5 – 9 kg average.
Remaining cakes – 30 kg total.
Also, as the average of the 9 < 30/x < 12.5. So, x = 3.
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Most Upvoted Answer
Mr. Baker runs a bakery shop. One day he made some cakes of differentw...
Solution:
Given data:
Let the weight of all cakes be x.
Weight of heaviest two cakes = 25% of x
Weight of lightest 5 cakes = 45% of x
Step 1: Calculation of weight of heaviest two cakes
Weight of heaviest two cakes = 25% of x
Let the weight of the heaviest cake be a and the weight of the second heaviest cake be b.
a + b = 0.25x …(1)
Step 2: Calculation of weight of lightest five cakes
Weight of lightest 5 cakes = 45% of x
Let the weight of the lightest cake be c and the weight of the second lightest cake be d and so on till e.
c + d + e + f + g = 0.45x …(2)
Step 3: Calculation of weight of remaining cakes
Total weight of all cakes = x
Weight of heaviest two cakes = a + b = 0.25x
Weight of lightest five cakes = c + d + e + f + g = 0.45x
Weight of remaining cakes = x - (a + b + c + d + e + f + g)
= x - 0.25x - 0.45x
= 0.3x
Step 4: Calculation of number of stolen cakes
The weight of all remaining cakes is 0.3x.
Let the weight of one cake be y.
Number of remaining cakes = (0.3x)/y
Mr. Baker sold the 5 lightest cakes and took the heaviest two cakes home.
Therefore, the weight of all remaining cakes is (x - a - b - c - d - e - f - g - 5c).
Hence, (x - a - b - c - d - e - f - g - 5c)/y = 0, which implies (x - a - b - c - d - e - f - g - 5c) = 0.
Thus, a + b + 5c = x - (c + d + e + f + g)
a + b + 5c = 0.55x …(3)
Substituting equation (1) in (3), we get:
0.25x + 5c = 0.55x
c = 0.06x
Substituting the value of c in equation (2), we get:
d + e + f + g = 0.39x
Substituting the value of c in equation (3), we get:
a + b = 0.3x
The weight of all remaining cakes is 0.3x.
The weight of one cake is 0.3x/(d+e+f+g).
Thus, the number of stolen cakes is:
(0.3x)/(0.39x) = 3.
Hence, the number of stolen cakes is 3.
Given data:
Let the weight of all cakes be x.
Weight of heaviest two cakes = 25% of x
Weight of lightest 5 cakes = 45% of x
Step 1: Calculation of weight of heaviest two cakes
Weight of heaviest two cakes = 25% of x
Let the weight of the heaviest cake be a and the weight of the second heaviest cake be b.
a + b = 0.25x …(1)
Step 2: Calculation of weight of lightest five cakes
Weight of lightest 5 cakes = 45% of x
Let the weight of the lightest cake be c and the weight of the second lightest cake be d and so on till e.
c + d + e + f + g = 0.45x …(2)
Step 3: Calculation of weight of remaining cakes
Total weight of all cakes = x
Weight of heaviest two cakes = a + b = 0.25x
Weight of lightest five cakes = c + d + e + f + g = 0.45x
Weight of remaining cakes = x - (a + b + c + d + e + f + g)
= x - 0.25x - 0.45x
= 0.3x
Step 4: Calculation of number of stolen cakes
The weight of all remaining cakes is 0.3x.
Let the weight of one cake be y.
Number of remaining cakes = (0.3x)/y
Mr. Baker sold the 5 lightest cakes and took the heaviest two cakes home.
Therefore, the weight of all remaining cakes is (x - a - b - c - d - e - f - g - 5c).
Hence, (x - a - b - c - d - e - f - g - 5c)/y = 0, which implies (x - a - b - c - d - e - f - g - 5c) = 0.
Thus, a + b + 5c = x - (c + d + e + f + g)
a + b + 5c = 0.55x …(3)
Substituting equation (1) in (3), we get:
0.25x + 5c = 0.55x
c = 0.06x
Substituting the value of c in equation (2), we get:
d + e + f + g = 0.39x
Substituting the value of c in equation (3), we get:
a + b = 0.3x
The weight of all remaining cakes is 0.3x.
The weight of one cake is 0.3x/(d+e+f+g).
Thus, the number of stolen cakes is:
(0.3x)/(0.39x) = 3.
Hence, the number of stolen cakes is 3.
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Mr. Baker runs a bakery shop. One day he made some cakes of differentweights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?Correct answer is '3'. Can you explain this answer?
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Mr. Baker runs a bakery shop. One day he made some cakes of differentweights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?Correct answer is '3'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Mr. Baker runs a bakery shop. One day he made some cakes of differentweights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?Correct answer is '3'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. Baker runs a bakery shop. One day he made some cakes of differentweights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?Correct answer is '3'. Can you explain this answer?.
Mr. Baker runs a bakery shop. One day he made some cakes of differentweights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?Correct answer is '3'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Mr. Baker runs a bakery shop. One day he made some cakes of differentweights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?Correct answer is '3'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. Baker runs a bakery shop. One day he made some cakes of differentweights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?Correct answer is '3'. Can you explain this answer?.
Solutions for Mr. Baker runs a bakery shop. One day he made some cakes of differentweights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?Correct answer is '3'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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