A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained, is
Started 5 days ago by Shashank in
Explanatory Answer
Since the total donation amount is 15,250 rupees, there should be at least one 250 rupee note. The remaining 15000 can exist as thirty 500 rupee notes.
Since the total donation amount is 15,250 rupees, there should be at least one 250 rupee note. The remaining 15000 can exist as thirty 500 rupee notes.
| Rs. 250 | Rs. 500 | Rs. 100 | Number of notes |
| 1 | 30 | 0 | 31 |
But the total number of notes will only be 31. We have 100 notes. So to keep the number of 500 notes as high as possible let’s convert the 500 rupee notes to 100 rupee notes. Every time we do this conversion we add 4 new notes.
| Rs. 250 | Rs. 500 | Rs. 100 | Number of notes |
| 1 | 30 | 0 | 31 |
| 1 | 29 | 5 | 35 |
| We add 4 new notes in each conversion, Our target is to reach 100 notes from 35 notes, the closest we can got to 100 by adding only 4’s to 35 is 99 99 = 35 + 4 (16) So this happens after 16 steps |
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| 1 | 13 | 85 | 99 |
From here, we can convert one 500 rupee note to two 250 rupee notes.
| 3 | 12 | 85 | 100 |
So, the maximum number of 500 rupee notes is 12
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