Two labourers A and B are together paid a total amount of Rs 650 per day. Labourer A is paid 160% of the amount paid to labourer B. How much (in Rs) is labourer B paid per day?

Introduction / Context:
This question involves percentage comparison between two quantities and total sum decomposition. It is a typical example from ratio and percentage topics, where one worker is paid a certain percent of the others wage, and the total payment is known. The idea is to express both payments in terms of one variable and then solve a simple equation.

Given Data / Assumptions:

• Total daily payment to A and B together = Rs 650.
• Payment to A is 160% of payment to B.
• We need to find the daily wage of B.

Concept / Approach:
If we let B's daily wage be x, then A's daily wage becomes 160% of x, that is 1.6x. The total wage per day for both is x + 1.6x = 2.6x, and this sum is given as Rs 650. Solving for x gives the wage of B. The problem is essentially a ratio problem where the effective ratio of A to B is 1.6 : 1, or 16 : 10, which simplifies to 8 : 5.

Step-by-Step Solution:
Step 1: Let daily wage of B be x. Step 2: Payment to A is 160% of x, so wage of A = 1.6x. Step 3: Total daily payment = x + 1.6x = 2.6x. Step 4: According to the question, 2.6x = 650. Step 5: So x = 650 / 2.6. Step 6: Compute x = 250. Step 7: Therefore, B is paid Rs 250 per day.

Verification / Alternative check:
Using the result x = 250, wage of B is 250 and wage of A is 160% of 250 = 1.6 * 250 = 400. The total becomes 250 + 400 = 650, which matches the given total. This confirms that the calculation is correct.

Why Other Options Are Wrong:

• 400: This is actually the wage of A, not B.
• 350: If B were paid 350, then A would get 1.6 * 350 = 560 and the total would be 910, not 650.
• 450: This value would lead to a total greater than 650 when A's wage is calculated.
• 300: With 300 for B, A would get 480 and the total 780, which is higher than 650.

Common Pitfalls:
Students may confuse 160% more with 160% of and treat it as A = B + 1.6B, which would be 260% of B instead of 160%. Here the wording clearly means A gets 160% of B's wage, that is 1.6 times B's wage. Another common issue is arithmetic errors in dividing 650 by 2.6. Converting 2.6 into a fraction like 26/10 can make the division easier.

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