A king wanted to reward his advisor, a wise man of the kingdom. So he asked the wiseman to name his own reward. The wiseman thanked the king but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days. Without making calculations, find how many coins will the advisor get in that month
Solution:
A king wanted to reward his advisor.
The King asked the wiseman to name his own reward.
The wiseman said that he would ask only for some gold coins each day for a month.
The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days.
We have to find the number of coins the advisor will get in that month.
The pattern is 1 + 3 + 5 + …… for 30 days.
We observe that it is the sum of odd numbers where the number of observations is 30 days.
We know that, sum of first n odd natural numbers = n²
Here, n = 30
So, sum of coins = (30)²
= 900
Therefore, the advisor asked for 900 gold coins in a month.
✦ Try This: Find all the perfect squares from 1 to 500 each of which is a sum of two perfect squares.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 129
A king wanted to reward his advisor, a wise man of the kingdom. So he asked the wiseman to name his own reward. The wiseman thanked the king but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days. Without making calculations, find how many coins will the advisor get in that month
Summary:
A king wanted to reward his advisor, a wise man of the kingdom. So he asked the wiseman to name his own reward. The wiseman thanked the king but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days. Without making calculations, the coins got by the advisor in that month is 900 coins.
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