Cindy bought 15 apples and 12 oranges and paid a sum of ₹447 for the purchase. Which of the statements given below is inconsistent with this information, leading to no possible prices of the two fruits?

Question

Accepted Answer

Let the price of one apple be x and one orange be y.

From the first purchase:
15x + 12y = 447  ---- (1)

Check each statement for consistency:

1) 25 apples and 20 oranges for ₹745:
25x + 20y = 745  ---- (2)

Multiply (1) by 5/3 to compare with (2):
(15x)(5/3) + (12y)(5/3) = 447 * 5/3
=> 25x + 20y = 745
This matches exactly with (2), so consistent.

2) 10 apples and 13 oranges for ₹353:
10x + 13y = 353  ---- (3)

Solve (1) and (3) to check for consistency:
From (1): 15x + 12y = 447
Multiply (3) by 3:
30x + 39y = 1059
Multiply (1) by 2:
30x + 24y = 894
Subtract:
(30x + 39y) - (30x + 24y) = 1059 - 894
15y = 165
=> y = 11
Substitute y=11 in (1):
15x + 12*11 = 447
15x + 132 = 447
15x = 315
x = 21
Check (3):
10*21 + 13*11 = 210 + 143 = 353
Matches perfectly, so consistent.

Wait, this suggests statement 2 is consistent, so we need to re-check.

3) 12 apples and 8 oranges for ₹340:
12x + 8y = 340  ---- (4)

Using x=21, y=11 from above:
12*21 + 8*11 = 252 + 88 = 340
Matches exactly, so consistent.

4) 35 apples and 28 oranges for ₹1029:
35x + 28y = 1029  ---- (5)

Using x=21, y=11:
35*21 + 28*11 = 735 + 308 = 1043
But given is 1029, which is different.

This means statement 4 is inconsistent.

Therefore, the inconsistent statement is option 4.

Answer

Answer

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