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NCERT Solutions for Class 5th Maths Chapter 6 Three ministers, three choices of gold — The King's Reward

Book page 88–89 Updated on2026-09-19

Q1.
Which of the rewards would you have chosen?
Answer

Sample answer: I would choose Choice 3 — take 1 gold coin and multiply the number of coins by 5 every day for 7 days. It ends with by far the most gold.

Here is the reasoning to share with the class.

  1. The starting number looks important, but it is not. Choice 1 starts with 5 coins, five times more than Choice 3. That head start is quickly wiped out.
  2. What matters is how fast the pile grows each day. Choice 1 grows 2 times a day, Choice 2 grows 3 times a day, Choice 3 grows 5 times a day.
  3. Multiplying again and again piles up very quickly. After seven days the fast-growing choice leaves the others far behind.
  4. So I would pick Choice 3.
A quick look at day 3
Choice 1: 5 → 10 → 20 → 40
Choice 2: 3 → 9 → 27 → 81
Choice 3: 1 → 5 → 25 → 125
Already the smallest start is winning.
Why the growth rate beats the head start: Every day, Choice 3 multiplies by 5 while Choice 1 multiplies by 2. Over seven days that difference is applied seven times over, and it overwhelms any head start.
Q2.
After a week, the 3 ministers were surprised at the final amount of gold coins. Guess who received the most gold coins? Calculate how much gold coins each minister received.
Answer

Minister 3 received the most: 78,125 gold coins. Minister 1 got 640 and Minister 2 got 6,561.

Work out each minister day by day.

DayMinister 1 (start 5, double)Minister 2 (start 3, triple)Minister 3 (start 1, × 5)
Start531
11095
2202725
34081125
480243625
51607293,125
63202,18715,625
76406,56178,125
Minister 1
Step 1. 5 doubled seven times.
Step 2. 5 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 5 × 128
Step 3. = 640 coins

Minister 2
Step 1. 3 tripled seven times.
Step 2. 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 3 × 2,187
Step 3. = 6,561 coins

Minister 3
Step 1. 1 multiplied by 5, seven times.
Step 2. 5 × 5 × 5 × 5 × 5 × 5 × 5
Step 3. = 78,125 coins
Why the surprise: Minister 1 began with five times as much gold as Minister 3, and still ended with less than one hundredth of it. When something is multiplied over and over, the size of the multiplier matters far more than the size of the start.
Try this: Work out what would happen on day 10 if the ministers kept going. Minister 3 would hold 5 × 5 × 5 more coins than on day 7 — that is 125 times 78,125. Repeated multiplying grows faster than almost anything else in mathematics.
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