When doing some shopping, the consumption tax is 5% of sales price and less than 1 yen is omitted.
For example, if sales price is 219 yen, 10 yen consumption tax will be cost and 229 yen will be paid.
When sales price is 220 yen, 231 yen will be paid.
Therefore, 230 yen does not emerge with the amount of money including the consumption tax.
Find an amount of money nearest to 1000 yen among those which do not emerge with the amount of money of including consumption tax.
Answer
1007 yen
Solution
In the case of 19 yen of the sales price, the amount of money including the consumption tax is 19 yen as 19 × 1.05 = 19.95.
In the case of 20 yen of the sales price, the amount of money including the consumption tax is 21 yen as 20 × 1.05 = 21.
From this, the smallest amount of money not to emerge with the amount of money including the consumption tax is 20 yen.
Next, the second smallest amount of money not to emerge with the amount of money including the consumption is 41 yen according to the calculation of 39 × 1.05 = 40.95 and 40 × 1.05 = 42.
The third is 62 yen according to the calculation of 59 × 1.05 = 61.95 and 60 × 1.05 = 63.
In this way, the amount of money that does not emerge as the amount of money including the consumption tax is to be found every 21 yen from 20 yen to 41 yen, 62 yen, ... .
Thus, the amount nearest to 1000 yen can be found in the number of 20 yen +21 yen × □.
(1000 - 20) / 21 = 46.6.
20 + 21 × 46 = 986, 20 + 21 × 47 = 1007.
It is 1,007 yen to be the nearest to 1,000 yen.
For example, if sales price is 219 yen, 10 yen consumption tax will be cost and 229 yen will be paid.
When sales price is 220 yen, 231 yen will be paid.
Therefore, 230 yen does not emerge with the amount of money including the consumption tax.
Find an amount of money nearest to 1000 yen among those which do not emerge with the amount of money of including consumption tax.
1007 yen
Solution
In the case of 19 yen of the sales price, the amount of money including the consumption tax is 19 yen as 19 × 1.05 = 19.95.
In the case of 20 yen of the sales price, the amount of money including the consumption tax is 21 yen as 20 × 1.05 = 21.
From this, the smallest amount of money not to emerge with the amount of money including the consumption tax is 20 yen.
Next, the second smallest amount of money not to emerge with the amount of money including the consumption is 41 yen according to the calculation of 39 × 1.05 = 40.95 and 40 × 1.05 = 42.
The third is 62 yen according to the calculation of 59 × 1.05 = 61.95 and 60 × 1.05 = 63.
In this way, the amount of money that does not emerge as the amount of money including the consumption tax is to be found every 21 yen from 20 yen to 41 yen, 62 yen, ... .
Thus, the amount nearest to 1000 yen can be found in the number of 20 yen +21 yen × □.
(1000 - 20) / 21 = 46.6.
20 + 21 × 46 = 986, 20 + 21 × 47 = 1007.
It is 1,007 yen to be the nearest to 1,000 yen.
