Question

Deepu has certain number of flowers. It is not less than 15 and not more than 30. If she wants to give these flowers equally to two of her friends. Then two flowers remain. If she wants to give these flowers equally to four of her friends, then three flowers remain. The number of flowers with Deepu is

Answer 1

Given :  

(i) Deepu has certain number of flowers.  

(ii) It is not less than 15 and not more than 30.

(iii) She wants give these flowers equally to four of her friends, then three flowers remain.

(iv) If she wants to give these flowers equally to THREE of her friends, then TWO flowers remain.

To find :

(i) The number of flowers with Deepu.

Solution:

For first case,

Flowers=  4y  + 3

For second case,

Flowers  = 3x  + 2

Now,

3x  + 2 = 4y + 3

⇒ 3(x - 1)  = 4y - 2

⇒ 3(x - 1) = 2(2y - 1)

⇒  3(x - 1) = 2(2y - 1) = 6k

⇒ x - 1 = 2k

⇒ x = 2k + 1    or  2y = 3k + 1

So,

3x + 2 = 3(2k + 1) + 2

= 6k + 5

And,

4y + 3 = 2(3k + 1) + 3

= 6k + 5

Therefore, flowers = 6k + 5

15 < 6k + 5  < 30

⇒ 10 < 6k  < 25

⇒ k = 2 , 3 , 4

Flowers = 17 , 23 , 29

So only 23 satisfies the conditions and hence this is the answer.

Deepu has 23 flowers.