Question 16 of 19intermediate🔧 ApplyNumerical4 marks

The Bakhshali Manuscript (300 CE) mentions the following problem. The amount given to the first person is not known. The second person is given twice as much as the first. The third person is given thrice as much as the second; and the fourth person four times as much as the third. The total amount distributed is 132. What is the amount given to the first person?

Correct Answer

Step 1: Let first person receive xx. Step 2: Second receives 2x2x, third receives 3×2x=6x3 \times 2x = 6x, fourth receives 4×6x=24x4 \times 6x = 24x. Step 3: Total: x+2x+6x+24x=33x=132x + 2x + 6x + 24x = 33x = 132. Step 4: Divide by 33: x=4x = 4.

Answer: The first person receives 4.

Verification: First person: 4 Second: 2×4=82 \times 4 = 8 Third: 3×8=243 \times 8 = 24 Fourth: 4×24=964 \times 24 = 96 Total: 4+8+24+96=1324 + 8 + 24 + 96 = 132 ∴ The solution is correct.

Exercise: Figure it Out (Section 3) | Q: 14 | (Page Page 25)
For More Understanding

Explanation

Let the first person receive xx. Then the second receives 2x2x, the third receives 3(2x)=6x3(2x) = 6x, and the fourth receives 4(6x)=24x4(6x) = 24x. Total: x+2x+6x+24x=33x=132x + 2x + 6x + 24x = 33x = 132, giving x=4x = 4.

Solution Steps

  1. Step 1: Let first person receive xx

  2. Step 2: Second receives 2x2x, third receives 3×2x=6x3 \times 2x = 6x, fourth receives 4×6x=24x4 \times 6x = 24x

  3. Step 3: Total: x+2x+6x+24x=33x=132x + 2x + 6x + 24x = 33x = 132

  4. Step 4: Divide by 33: x=4x = 4

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