Question

Ram packs sweets in such a way that if he packs 20 in each box, there would be 15 sweets left. if he packs 25 each, there would be 20 sweets left, if he packs 38 each, there would be 33 sweets left and if he packs 40 sweets in each box, there would be 35 sweets left. what is the minimum number of sweets the person have?

Answer 1

20....................................

Answer 2

The minimum number of sweets the person can have is 3795.

Given:

Ram packs sweets in a box in such a way that,

If he packs 20 in each box, there would be 15 sweets left.

If he packs 25 each, there would be 20 sweets left.

If he packs 38 each, there would be 33 sweets left.

If he packs 40 sweets in each box, there would be 35 sweets left.

To Find:

The minimum number of sweets Ram has with him =?

Solution:

The above question is from the topic of the number system.

Here, to calculate the minimum value of the number of sweets that ram can have we need to be familiar with the concept of LCM.

LCM of two numbers i.e., lowest common multiple of two numbers is defined as that number which on dividing with either number returns zero as the remainder.

Here, as we can see the number of sweets left to pack in the box is five less than the total number of sweets in each box.

i.e., If 'p' is the minimum number of sweets, then;

p = 20x₁ + 15

p = 25x₂ + 20

p = 38x₃ + 33

p = 40x₄ + 35

Here, all the divisors are five more than the remainder.

So, our required answer is [LCM (20, 25, 38, 40) -5]

Now, the LCM of the four numbers is 3800 as it is their lowest common multiple.

required answer = 3800 - 5

∴ Answer = 3795

Thus, The minimum number of sweets Ram has with him is 3795.

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