Suppose you are collecting money for something. You need ₹ 200 in all. You ask your parents, uncles and aunts

Exercise · Q5

Q. Suppose you are collecting money for something. You need ₹ 200 in all. You ask your parents, uncles and aunts as well as grandparents. Different people may give either ₹ 10, ₹ 20 or even ₹ 50. You will collect till the total becomes 200. Write the algorithm.

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Concept understanding — Addition Algorithm

Addition Algorithm: What It Is and Why It Works

Imagine you have 27 marbles and your friend has 15. You want to know the total. You could count them one by one — but that's slow. The addition algorithm is the step-by-step method we use to add numbers quickly and reliably, even when they're huge.

The word "algorithm" just means a clear, repeatable procedure. The addition algorithm is the one you learned in school: line up the numbers by place value, add column by column from right to left, and "carry" when a column's sum reaches ten or more.

The Intuition: Why We Carry

Think of base-ten blocks. A "ten" is a bundle of ten ones. When you add 27 and 15:

7 ones + 5 ones = 12 ones. That's one ten and two leftover ones.
So you bundle those ten ones into a new ten, and move it to the tens column.
Then you add the tens: 2 tens + 1 ten + that extra ten = 4 tens.
Result: 4 tens and 2 ones = 42.

The "carry" is just bundling. Every time a column's sum hits ten or more, you form a group of ten and shift it left. That's all.

The Precise Statement

Addition Algorithm (for whole numbers) To add two or more numbers: Write them vertically, aligning digits by place value (ones under ones, tens under tens, etc.). Starting from the rightmost column (the ones place), add the digits in that column. If the sum is less than 10, write it below the column. If the sum is 10 or more, write the ones digit of the sum below the column, and carry the tens digit to the next column to the left. Repeat for each column moving left. If a column has no digits, treat it as 0. The final number written below is the sum.

A Worked Example

Add 358 and 476.

  358
+ 476
-----

Start with the ones column: $8 + 6 = 14$ . Write 4, carry 1 to the tens column.

  1
  358
+ 476
-----
    4

Tens column: $5 + 7 + 1 = 13$ . Write 3, carry 1 to the hundreds column.

 1 1
  358
+ 476
-----
   34

Hundreds column: $3 + 4 + 1 = 8$ . Write 8.

 1 1
  358
+ 476
-----
  834

Result: $358 + 476 = 834$ .

Tip

The carry is always at most 1 when adding two digits (since $9+9=18$ ). But when adding many numbers, a column can sum to 20 or more — then you carry the tens digit (e.g., sum 23 means carry 2, write 3).

Why This Works (The Math Behind It)

The algorithm works because of place value and the distributive property. Every number is a sum of its digits times powers of ten:

358 = 3 \times 100 + 5 \times 10 + 8 \times 1

476 = 4 \times 100 + 7 \times 10 + 6 \times 1

Adding them:

$(3+4) \times 100 + (5+7) \times 10 + (8+6) \times 1$ …

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Keep a running total and keep accepting contributions while it is below 200:

COLLECT_MONEY
    SET total = 0
    WHILE total < 200
        INPUT amount        (10, 20 or 50)
        total = total + amount
    END WHILE
    PRINT "Target reached! Total collected =", total
END
``` …

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A condition-controlled accumulation loop: start total at 0, keep reading each person's gift and adding it, and stop as soon as total reaches 200.

The idea (accumulation). We do not know how many people will contribute — only when to stop (total = 200). That calls for a condition-controlled loop with an accumulator: a variable total that starts at 0 and grows by each input amount. The loop condition total < 200 is checked before every new request, so we stop asking the moment the target is met.

Algorithm

COLLECT_MONEY_ALGO
Step 1: SET total = 0
Step 2: WHILE total < 200, REPEAT Steps 3-4
Step 3:     INPUT amount        (a person gives 10, 20 or 50)
Step 4:     total = total + amount
Step 5: PRINT "Target reached! Total collected =", total
END

Python implementation

total = 0
while total < 200:
    amount = int(input("Amount given (10/20/50): "))
    total = total + amount
print("Target reached! Total collected =", total)

Dry run for contributions 50, 50, 20, 50, 20, 10:

Person	amount	total after adding	total < 200? (next test)
1	50	50	yes — ask again
2	50	100	yes
3	20	120	yes
4	50	170	yes
5	20	190	yes

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Q.Suppose you are collecting money for something. You need ₹ 200 in all. You ask your parents, uncles and aunts as well as grandparents. Different people may give either ₹ 10, ₹ 20 or even ₹ 50. You will collect till the total becomes 200. Write the algorithm.

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