Question

Sumit was doing a multiplication, but by mistake instead of taking 25 as one of the multiplier, he took 34. Now, because of this mistake, the answer was 405 more than the correct answer. Find out the answer that Sumit arrived at.

• A. 1530
• B. 1450
• C. 1350
• D. 1620

Answer 1

The Correct Option is A

Let's denote the correct product by \( P \) and the multiplicand by \( x \).
Sumit’s mistake was using 34 instead of 25. The incorrect product is:
\[ 34x = 25x + 405 \]
This implies:
\[ 34x - 25x = 405 \]
\[ 9x = 405 \]
\[ x = 45 \]
The correct product is:
\[ 25x = 25 \times 45 = 1125 \]
The incorrect product Sumit arrived at is:
\[ 34x = 34 \times 45 = 1530 \]
Therefore, Sumit’s incorrect answer is:
Answer: A (1530)

Answer 2

Instead of building an equation, we can test each option directly and see which one is consistent with the 405 excess caused by using 34 instead of 25.

1. Option A (1530): If Sumit's wrong answer is 1530, the number he multiplied is \( 1530 \div 34 = 45 \). Checking the gap: \( (34 - 25) \times 45 = 9 \times 45 = 405 \), which matches the given excess exactly.
2. Option B (1450): This would need a number of \( 1450 \div 34 \approx 42.6 \), and \( 9 \times 42.6 \approx 383.8 \), not 405.
3. Option C (1350): This would need a number of \( 1350 \div 34 \approx 39.7 \), and \( 9 \times 39.7 \approx 357.4 \), not 405.
4. Option D (1620): This would need a number of \( 1620 \div 34 \approx 47.6 \), and \( 9 \times 47.6 \approx 428.8 \), not 405.

Only option A gives a gap of exactly 405 when the multiplier changes from 25 to 34, so this is the value Sumit actually got.

Let's summarize:

• The multiplier gap of 9 alone explains the full 405 excess.
• Dividing 405 by that gap gives the number Sumit was multiplying.

Therefore, the correct answer is A (1530).