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?

Let N50, N20, and N10 be the number of notes of denominations ₹50, ₹20, and ₹10 respectively.

Given: Total amount = 50N50 + 20N20 + 10*N10 = 1840 Total number of notes = N50 + N20 + N10 = 50

Let's analyze each statement:

Statement 1: 25 notes of ₹50 are used (N50 = 25). Substitute N50 = 25 into the equations:

1. 5025 + 20N20 + 10N10 = 1840 => 1250 + 20N20 + 10N10 = 1840 => 20N20 + 10*N10 = 590
2. 25 + N20 + N10 = 50 => N20 + N10 = 25

From the second derived equation, N10 = 25 - N20. Substitute this into the first derived equation: 20N20 + 10(25 - N20) = 590 20N20 + 250 - 10N20 = 590 10*N20 = 340 N20 = 34

Now find N10: N10 = 25 - 34 = -9. Since the number of notes cannot be negative, Statement 1 is incorrect.

Statement 2: 35 notes of ₹20 are used (N20 = 35). Substitute N20 = 35 into the equations:

1. 50N50 + 2035 + 10N10 = 1840 => 50N50 + 700 + 10N10 = 1840 => 50N50 + 10*N10 = 1140
2. N50 + 35 + N10 = 50 => N50 + N10 = 15

From the second derived equation, N10 = 15 - N50. Substitute this into the first derived equation: 50N50 + 10(15 - N50) = 1140 50N50 + 150 - 10N50 = 1140 40*N50 = 990 N50 = 990 / 40 = 24.75

Since the number of notes must be an integer, Statement 2 is incorrect.

Statement 3: 20 notes of ₹10 are used (N10 = 20). Substitute N10 = 20 into the equations:

1. 50N50 + 20N20 + 1020 = 1840 => 50N50 + 20N20 + 200 = 1840 => 50N50 + 20*N20 = 1640
2. N50 + N20 + 20 = 50 => N50 + N20 = 30

From the second derived equation, N20 = 30 - N50. Substitute this into the first derived equation: 50N50 + 20(30 - N50) = 1640 50N50 + 600 - 20N50 = 1640 30*N50 = 1040 N50 = 1040 / 30 = 104 / 3 = 34.66...

Since the number of notes must be an integer, Statement 3 is incorrect.

Since all three statements (1, 2, and 3) are incorrect, the correct option is D.

The final answer is D