A bill for $1,840$ is paid in the denominations of $50$, $20$ and $10$ notes. $50$ notes in all are used. Consider the following statements: 1. $25$ notes of $50$ are used and the remaining are in the denominations of $20$ and $10$. 2. $35$ notes of $20$ are used and the remaining are in the denominations of $50$ and $10$. 3. $20$ notes of $10$ are used and the remaining are in the denominations of $50$ and $20$. Which of the above statements are not correct?

QUESTION

CSAT

Medium

Maths

Prelims 2022

A bill for $1,840$ is paid in the denominations of $50$ , $20$ and $10$ notes. $50$ notes in all are used. Consider the following statements:

$25$ notes of $50$ are used and the remaining are in the denominations of $20$ and $10$ .
$35$ notes of $20$ are used and the remaining are in the denominations of $50$ and $10$ .
$20$ notes of $10$ are used and the remaining are in the denominations of $50$ and $20$ .

Which of the above statements are not correct?

Select an option to attempt

Explanation

Given: Total amount = ₹1,840 Number of notes = 50 Denominations available = ₹50, ₹20, and ₹10 Let the number of ₹50, ₹20, and ₹10 notes be x, y, and z respectively. Thus, we have: $50x + 20y + 10z = 1840$

Statement 1: 25 notes of ₹50 denomination were used. If 25 notes of ₹50 are used, the total from these notes would be: $25 \times 50 = 1250$ Remaining amount: $1840 - 1250 = 590$ Remaining notes: $50 - 25 = 25$ Even if we use all 25 remaining notes as ₹20 notes (the highest denomination left), the total would be: $25 \times 20 = 500$ This only sums to ₹1,750, which is short of ₹1,840. Therefore, Statement 1 is incorrect.
Statement 2: 35 notes of ₹20 denomination were used. If 35 notes of ₹20 are used, the total from these notes would be: $35 \times 20 = 700$ Remaining amount: $1840 - 700 = 1140$ Remaining notes: $50 - 35 = 15$ Even if we use all 15 remaining notes as ₹50 notes (the highest denomination left), the total would be: $15 \times 50 = 750$ This only sums to ₹1,450, which is again short of ₹1,840. Therefore, Statement 2 is also incorrect.
Statement 3: 20 notes of ₹10 denomination were used. If 20 notes of ₹10 are used, the total from these notes would be: $20 \times 10 = 200$ Remaining amount: $1840 - 200 = 1640$ Remaining notes: $50 - 20 = 30$ Even if we use all 30 remaining notes as ₹50 notes (the highest denomination left), the total would be: $30 \times 50 = 1500$ This only sums to ₹1,700, which is again short of ₹1,840. Therefore, Statement 3 is also incorrect.