Two labourers, A and B, are paid a total of Rs. 650 per day. Labourer A is paid 160% of what B is paid. How much, in rupees, is labourer B paid per day?

Introduction / Context:
This question is a typical example of percentage comparison between two incomes where their combined total is also given. It asks you to find the individual share of one labourer when the total daily payment and a percentage relation between their wages are known. Such questions are very common in aptitude exams, especially in topics like ratio, proportion, and percentage.

Given Data / Assumptions:

• Total payment to labourers A and B together per day = Rs. 650.
• Payment to A is 160% of the payment to B.
• We need to find the daily wage of B.
• All amounts are per day, and there are only two labourers considered.

Concept / Approach:
Let the payment to B be some variable, say x rupees. Since A earns 160% of B, the payment to A is 160% of x, which is (160 / 100) * x = 1.6x. The total payment is then x + 1.6x. We know that this sum equals 650. This gives a simple linear equation in x which we can solve. Once x is found, that value represents the payment of B.

Step-by-Step Solution:
Step 1: Let the daily wage of B be x rupees. Step 2: Since A is paid 160% of B, wage of A = 1.6x rupees. Step 3: Total daily wages of A and B together is x + 1.6x. Step 4: According to the question, x + 1.6x = 650. Step 5: Combine like terms to get 2.6x = 650. Step 6: Solve for x: x = 650 / 2.6. Step 7: Calculate 650 / 2.6 = 250. Step 8: Therefore, B is paid Rs. 250 per day.

Verification / Alternative check:
Let us verify by finding A's wage from this value. If B earns Rs. 250, then A earns 160% of 250, which is (160 / 100) * 250 = 1.6 * 250 = 400. Now, total wages = 250 + 400 = 650, which matches the given total payment. Therefore the calculated value for B's wage is consistent and correct.

Why Other Options Are Wrong:
If B earned Rs. 400, A would earn 160% of 400, or 640, and their total would be 1040, not 650. If B earned Rs. 350, A would earn 560, total 910. If B earned Rs. 450, A would earn 720, total 1170. None of these totals match the given Rs. 650. Only Rs. 250 for B produces the correct total.

Common Pitfalls:
A common misunderstanding is to treat 160% as 1.60 times without connecting properly to the total. Some learners mistakenly think A's wage is 160% more than B (which would be 260% of B) instead of 160% of B. Reading the phrase carefully is crucial. Also, performing mental division in the last step may lead to arithmetic mistakes, so writing the calculation clearly as 650 / 2.6 is helpful.

Final Answer:
Labourer B is paid Rs. 250 per day.