Question
Download Solution PDFComprehension
Directions: Read the data carefully and answer the following questions.
Three people – Aman, Bhavna, and Chirag – were assigned the task of taking printouts of some documents. Each of them printed documents both in black & white and in colour. No document was printed by more than one person.
The total number of printouts taken by all three persons together is 700. Aman took 200 printouts, out of which 70% were black & white printouts. The ratio of colour printouts taken by Aman, Bhavna, and Chirag is 1 :2 : 3. The number of colour printouts taken by Bhavna is 20% more than the number of black & white printouts taken by her. The number of black & white printouts taken by Bhavna and Chirag is the same.
Under new rules of submission of printouts, for every 3 color printouts, Aman can submit only 2 B&W printouts. Calculate the maximum printouts Aman can submit.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGeneral Solution:
Total printouts by all three: 700
Aman's printouts:
Total: 200
70% B&W, so 30% color
B&W: 0.7 × 200 = 140
Color: 0.3 × 200 = 60
Ratio of color printouts by Aman : Bhavna : Chirag = 1 : 2 : 3
Aman's color printouts = 60 (from above)
So, ratio 1 part = 60
Therefore:
Bhavna's color = 2 × 60 = 120
Chirag's color = 3 × 60 = 180
Bhavna's color printouts are 20% more than her B&W printouts:
Let Bhavna's B&W = x
Then, color = x + 0.2x = 1.2x
We know color = 120, so:
1.2x = 120
x = 120 / 1.2 = 100
So, Bhavna's B&W = 100, color = 120
Total for Bhavna: 100 + 120 = 220
Bhavna and Chirag have the same number of B&W printouts:
Bhavna's B&W = 100, so Chirag's B&W = 100
Chirag's color = 180 (from ratio)
Total for Chirag: 100 + 180 = 280
Let's check the total printouts:
Aman: 200
Bhavna: 220
Chirag: 280
Total: 200 + 220 + 280 = 700 (matches given)
Summary of Printouts:
Aman:
B&W: 140
Color: 60
Total: 200
Bhavna:
B&W: 100
Color: 120
Total: 220
Chirag:
B&W: 100
Color: 180
Total: 280
Calculations:
Aman can submit 2 black & white (B&W) printouts for every 3 color printouts.
Aman's Printouts:
B&W: 140
Color: 60
Maximum B&W based on colors:
Aman has 60 color printouts.
He can submit = (2/3) × 60 = 40 B&W printouts based on his color printouts.
Compare to actual B&W: Aman has 140 B&W printouts but he can only submit 40 based on his colors.
Total submissions:
He can submit all 60 color printouts.
He can only submit 40 black and white printouts.
Total Submissions: 60 + 40 = 100
Thus, the maximum printouts Aman can submit is 100.
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