Rajesh had to arrange his books in uniform groups. He makes groups of 4 books each. But 3 books are left. He tries it with groups of 5 books each. But still 3 books are left. 3 books are still left when he tried with groups of 9 or 10 books each. How many books does he have?a)90b)180c)900d)183e)None of theseCorrect answer is option 'D'. Can you explain this answer?

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Rajesh had to arrange his books in uniform groups. He makes groups of 4 books each. But 3 books are left. He tries it with groups of 5 books each. But still 3 books are left. 3 books are still left when he tried with groups of 9 or 10 books each. How many books does he have?

a)
90
b)
180
c)
900
d)
183
e)
None of these

Correct answer is option 'D'. Can you explain this answer?

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Rajesh had to arrange his books in uniform groups. He makes groups of ...

Since we need total number of books, we must find LCM of 4,5,9,10

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Rajesh had to arrange his books in uniform groups. He makes groups of ...

Given:
Rajesh tries to make groups of 4, 5, 9, and 10 books. In all attempts, 3 books are left.

To find:
The total number of books Rajesh has.

Solution:
Let's assume that the total number of books Rajesh has is 'x'.

When Rajesh tries to make groups of 4 books each, he is left with 3 books.
So, the total number of books can be represented as 4a + 3, where 'a' is a whole number.

Similarly, when Rajesh tries to make groups of 5 books each, he is left with 3 books.
So, the total number of books can be represented as 5b + 3, where 'b' is a whole number.

Again, when Rajesh tries to make groups of 9 books each, he is left with 3 books.
So, the total number of books can be represented as 9c + 3, where 'c' is a whole number.

Finally, when Rajesh tries to make groups of 10 books each, he is left with 3 books.
So, the total number of books can be represented as 10d + 3, where 'd' is a whole number.

We can write all these equations as follows:

4a + 3 = 5b + 3 = 9c + 3 = 10d + 3

Subtracting 3 from both sides of each equation, we get:

4a = 5b = 9c = 10d

Now, we need to find the smallest number that is divisible by 4, 5, 9, and 10.

The LCM of 4, 5, 9, and 10 is 180. So, we can write:

4a = 5b = 9c = 10d = 180

Solving for 'a', 'b', 'c', and 'd', we get:

a = 45, b = 36, c = 20, d = 18

Substituting these values in any of the equations, we get:

x = 4a + 3 = 5b + 3 = 9c + 3 = 10d + 3 = 183

Therefore, Rajesh has 183 books.

Answer: Option D.

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