Umesh took 100 chocolates out of 250 chocolates from Ruchi. Umesh gave 20% of his chocolates to Shalaka and 35% of his chocolates to Mary. Then Ruchi gave 50% of her remaining chocolates to Umesh. Find the number of chocolates Umesh had at the end.
120
Calculating Umesh's Final Chocolate Count
This solution explains the step-by-step process to determine the total number of chocolates Umesh possesses at the end, based on the transactions described.
Initial Distribution
The problem starts with Ruchi having 250 chocolates. Umesh takes 100 of these chocolates.
- Total chocolates initially with Ruchi = 250
- Chocolates Umesh took = 100
- Chocolates remaining with Ruchi = Total chocolates - Chocolates Umesh took
- Chocolates remaining with Ruchi = \(250 - 100 = 150\)
- Chocolates Umesh has initially = 100
Umesh Gives Chocolates Away
Umesh then distributes a percentage of his chocolates to Shalaka and Mary. The percentages are calculated based on the 100 chocolates Umesh initially took.
- Percentage given to Shalaka = \(20\%\)
- Amount given to Shalaka = \(20\%\) of 100 = \(\frac{20}{100} \times 100 = 20\) chocolates.
- Percentage given to Mary = \(35\%\)
- Amount given to Mary = \(35\%\) of 100 = \(\frac{35}{100} \times 100 = 35\) chocolates.
- Total chocolates given away by Umesh = Amount to Shalaka + Amount to Mary
- Total chocolates given away by Umesh = \(20 + 35 = 55\) chocolates.
- Chocolates Umesh has after giving away = Initial chocolates Umesh had - Total given away
- Chocolates Umesh has after giving away = \(100 - 55 = 45\) chocolates.
Ruchi's Contribution
Next, Ruchi gives a portion of her remaining chocolates back to Umesh.
- Chocolates Ruchi had remaining = 150
- Percentage Ruchi gave to Umesh = \(50\%\)
- Amount Ruchi gave to Umesh = \(50\%\) of 150 = \(\frac{50}{100} \times 150 = 75\) chocolates.
Final Calculation
To find the final number of chocolates Umesh has, we add the chocolates he received from Ruchi to the chocolates he had left after his own distribution.
- Chocolates Umesh had after giving away = 45
- Chocolates Umesh received from Ruchi = 75
- Final number of chocolates Umesh had = Chocolates after giving away + Chocolates received from Ruchi
- Final number of chocolates Umesh had = \(45 + 75 = 120\) chocolates.
Therefore, Umesh had 120 chocolates at the end.
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