Averages , Ratio and Proportion Question 9 - CAT 2024
A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is:
Step-by-Step Explanation
Work backward step-by-step from the final state of 0 kg:
- Step 3 (Reverse Customer 3):
Before the final sale, the shop added 3 kg and then doubled the quantity because it had sold half:
Quantity = (0 + 3) × 2 = 6 kg
- Step 2 (Reverse Customer 2):
Apply the same reverse operation to the remaining balance from the second sale:
Quantity = (6 + 3) × 2 = 18 kg
- Step 1 (Reverse Customer 1):
Apply the operation one last time to find the initial starting quantity:
Initial Quantity = (18 + 3) × 2 = 42 kg
Correct Option: C
💡 FundaMakers Tip:
For multi-stage subtraction problems that end at zero, always work backward from the final step. The inverse operation of "subtracting half and then subtracting 3" is "adding 3 and then doubling". Applying this simple rule step-by-step eliminates the need for complex algebraic equations.