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After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equal distribution. What was the total number of sweets?
  • a)
    328                                     
  • b)
    348                         
  • c)
    358                                     
  • d)
    Data inadequate
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
After distributing the sweets equally among 25 children, 8 sweets rema...
Let the total number of sweets be (25x + 8).
Then, (25x +8)-22 is divisible by 28
(25x -14) is divisible by28
28x - (3x +14) is divisible by 28
(3x + 14) is divisible by 28
∴ x = 14
Total number of sweets = (25x 14+ 8)
= 358 
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Most Upvoted Answer
After distributing the sweets equally among 25 children, 8 sweets rema...
Understanding the Problem
To find the total number of sweets, let’s denote the total number of sweets as S. We have two scenarios given in the problem:
1. Scenario with 25 Children
- Each child receives an equal number of sweets.
- 8 sweets remain after distribution.
- This can be expressed as:
S = 25x + 8 (where x is the number of sweets each child receives)
2. Scenario with 28 Children
- Each child also receives an equal number of sweets.
- 22 sweets remain after distribution.
- This can be expressed as:
S = 28y + 22 (where y is the number of sweets each child receives)
Setting Up the Equations
Now we have two equations based on the above scenarios:
- From the first scenario:
S = 25x + 8
- From the second scenario:
S = 28y + 22
Since both equations equal S, we can set them equal to each other:
25x + 8 = 28y + 22
Simplifying the Equation
Rearranging gives us:
25x - 28y = 14
This equation shows a relationship between x and y. We can find integer solutions for x and y.
Finding Solutions
From the equation, let’s express y in terms of x:
28y = 25x - 14
y = (25x - 14) / 28
For y to be an integer, (25x - 14) must be divisible by 28. Testing different values of x gives:
- If x = 4, then:
y = (25*4 - 14) / 28 = 2
Now, substituting x = 4 back into either equation to find S:
S = 25(4) + 8 = 100 + 8 = 108
To find the total number of sweets, substitute different x values until S is consistent with both equations.
Finally, we find that S = 358 is valid for x = 14 and y = 12.
Conclusion
Thus, the total number of sweets is:
Correct Answer: 358 (Option C)
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Direction: Read the passage and answer the question based on it.The Public Distribution System (PDS) was set up in India originally as a rationing system to cope with the food shortages during the Second World War period. From 1965, it was expanded into a universal system for delivering cheap food grain such as wheat and rice and certain other essential commodities such as sugar, edible oil, and kerosene. While the major objective of the PDS has been to act as a welfare measure to provide these goods at prices that are relatively lower than the market, it has also acted as a countervailing force to prevent speculation in prices by profit-oriented private traders. Since the PDS constitutes a major outlet for the sale of grain procured by the procurement agencies, it is an important link in the support system provided to farmers by the government. Over the years, the buffer stocks maintained by the PDS have served to ensure price stability and self-sufficiency in food even in years of severe drought and thereby helped to maintain the economic sovereignty of the country.What is PDS and what was its origin?

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After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equal distribution. What was the total number of sweets?a)328b)348c)358d)Data inadequateCorrect answer is option 'C'. Can you explain this answer?
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