Khushi buys bangles of three types at prices of Rs 34 per piece, Rs 42 per piece, and Rs 6 per piece. She buys an equal number of bangles of each type and spends a total of Rs 1,722 on all the bangles together. How many bangles did she buy of each type?

Introduction / Context:
This arithmetic reasoning question involves equal quantities and total cost. Khushi buys three kinds of bangles at different prices per piece, but the number of bangles of each type is the same. You are told her total expenditure, and you must find the number of bangles of each type. This is a straightforward application of linear equations with one variable.

Given Data / Assumptions:

• Type 1 bangles cost Rs 34 per piece.
• Type 2 bangles cost Rs 42 per piece.
• Type 3 bangles cost Rs 6 per piece.
• She buys the same number of bangles of each type.
• Total amount spent on all bangles is Rs 1,722.
• The answer asks for the number of bangles of each type, not the total number of bangles.

Concept / Approach:
Let Khushi buy n bangles of each type. Then the total number of bangles is 3n. The total cost is the sum of cost per type: n times the sum of the three prices. This gives a simple equation in n, which we can solve by dividing the total amount by the combined cost per set of one of each type. Because n must be an integer, we also check that the division is exact.

Step-by-Step Solution:
Step 1: Let the number of bangles of each type be n. Step 2: Cost of type 1 bangles = 34n, cost of type 2 bangles = 42n, and cost of type 3 bangles = 6n. Step 3: Total cost = 34n + 42n + 6n = (34 + 42 + 6)n = 82n. Step 4: The total cost is given as Rs 1,722, so 82n = 1,722. Step 5: Solve for n: n = 1,722 / 82. Step 6: 1,722 ÷ 82 = 21. Step 7: Therefore, Khushi bought 21 bangles of each type.

Verification / Alternative check:
Compute total cost using n = 21: cost of type 1 = 34 * 21 = 714, cost of type 2 = 42 * 21 = 882, cost of type 3 = 6 * 21 = 126. Sum: 714 + 882 + 126 = 1,722, which matches the given expenditure. This confirms that the value n = 21 is correct.

Why Other Options Are Wrong:
Option A 27 gives total cost 82 * 27 = 2,214, too high. Option B 13 gives total cost 82 * 13 = 1,066, too low. Option C 17 gives 82 * 17 = 1,394, which also does not equal 1,722. None of these options produce the correct total cost.

Common Pitfalls:
Some students mistakenly multiply 1,722 by 3 or divide by only one of the prices instead of the combined price per set of three bangles. Another error is to miscalculate the sum of 34, 42, and 6. Carefully summing the three prices before dividing the total amount keeps the algebra simple and reliable.

Final Answer:
Khushi bought 21 bangles of each type.