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If a farmer packs 8 or 11 mangoes in a box, he is left with 5 mangoes. But if he packs 6 or 7 mangoes in each box also he is left with 5 mangoes. Find the no. of mangoes that he had 
  • a)
    2645 
  • b)
    1853 
  • c)
    2520 
  • d)
    1545 
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If a farmer packs 8 or 11 mangoes in a box, he is left with 5 mangoes....
LCM of 8, 11, 6 and 7
= 1848
Required number of mangoes = 1848 + 5 = 1853
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Most Upvoted Answer
If a farmer packs 8 or 11 mangoes in a box, he is left with 5 mangoes....
Given:
- The farmer packs either 8 or 11 mangoes in a box and is left with 5 mangoes.
- The farmer also packs either 6 or 7 mangoes in a box and is left with 5 mangoes.

To find:
The total number of mangoes the farmer had.

Approach:
Let's assume that the total number of mangoes the farmer had is 'x'. We can solve the problem using the following steps:

1. When the farmer packs 8 mangoes in a box:
- The number of boxes required = x / 8
- The total mangoes packed = (x / 8) * 8 = 8(x / 8) = x
- The number of mangoes left = 5

2. When the farmer packs 11 mangoes in a box:
- The number of boxes required = x / 11
- The total mangoes packed = (x / 11) * 11 = 11(x / 11) = x
- The number of mangoes left = 5

3. When the farmer packs 6 mangoes in a box:
- The number of boxes required = x / 6
- The total mangoes packed = (x / 6) * 6 = 6(x / 6) = x
- The number of mangoes left = 5

4. When the farmer packs 7 mangoes in a box:
- The number of boxes required = x / 7
- The total mangoes packed = (x / 7) * 7 = 7(x / 7) = x
- The number of mangoes left = 5

From the given conditions, we can form two equations as follows:

Equation 1: x = 8a + 5 (where a is the number of boxes packed with 8 mangoes)
Equation 2: x = 11b + 5 (where b is the number of boxes packed with 11 mangoes)

Solution:
To find the total number of mangoes, we need to find the common solution of the above two equations.

By solving these equations, we get the value of x as 1853.

Therefore, the correct answer is option 'B' (1853).
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