There are 3 pencil boxes containing 3 colored pendls – Red, Green and Blue.
Pencil box 1 contains: 24 green pencils. Red pencils are 4 more than blue pencils. Probability
of selecting 1 red pencil is 4/13
Pencil box 2 contains: Total pencils are 8 more than 7/13 of pencils in pencil box 1. Probability
of selecting 1 red pendl is 1/3. The ratio of green pencils to blue pencils is 1:2
Pencil box 3 contains: Red pencils equal total number of green and blue penclls in pencil box
2. Green
pencils equal total number of green and red pencils in pencil box 2. Probability of selecting 1
blue pencil is 3/14.
Some green pencils are transferred from pencil box 1 to pencil box 3. Now probability of
choosing a blue pencil from pencil box 3 becomes 3/16. Find the number of remaining pencils
in pencii box 1.
Answers
Given : There are 3 pencil boxes containing 3 colored pencils – Red, Green and Blue.
To find : the number of remaining pencils in pencii box 1.
Solution:
Pencil box 1 contains:
Green pencils = 24
Red pencils = B + 4
Blue Pencils = B
Total Pencils = 2B + 28
Probability of selecting 1 red pencil = (B + 4 )/(2B + 28) = 4/13
=> 13B + 52 = 8B + 112
=> 5B = 60
=> B = 12
Pencil Box 1 :
Green pencils = 24 , Red pencils = 16 , Blue Pencils = 12 ,
Total Pencils = 52
Pencil box 2 contains:
Total pencils are 8 more than 7/13 of pencils in pencil box 1.
=> Total Pencils in Box 2 = 8 + (7/13)52 = 36
Probability of selecting 1 red pencil is 1/3 => Red Pencils = 12
Green Pencil to Blue pencil Ratio 1 : 2
Green Pencil = 8 , Blue Pencil = 16
Pencil Box 2 :
Green pencils = 8 , Red pencils = 12 , Blue Pencils = 16 ,
Total Pencils = 36
Pencil box 3 contains:
Red Pencils = Green + Blue Pencils in box 2 = 8 + 16 = 24
Green pencils = Green + Red pencils in pencil box 2 = 8 + 12 = 20
Probability of selecting 1 blue pencil is 3/14. => B/(B + 44) = 3/14
=> 14B = 3B + 132 => 11B = 132 => B = 12
Pencil Box 3 :
Green pencils = 20 , Red pencils = 24 , Blue Pencils = 12 ,
Total Pencils = 56
Some green pencils are transferred from pencil box 1 to pencil box 3.
Total = 56 + G
12/(56 + G) = 3/16
=> 192 = 168 + 3G
=> 3G = 24
=> G = 8
8 Pencils transferred from Pencil Box 1 to Pencil Box 3
52 - 8 = 44 number of remaining pencils in pencil box 1.
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Number of remaining pencils in Box 1 = 44
Step-by-step explanation:
Given: There are 3 pencil boxes containing 3 colored pencils - Red, Green and Blue.
Find: The number of remaining pencils in pencil box 1.
Solution:
Box 1 = 28 + 2x
24 Green
Let number of blue pencils be x.
Red pencils = x + 4
Probability of selecting 1 red pencil = (x + 4 ) / (2x + 28) = 4/13
13(x+4) = 4 (2x+28)
13x + 52 = 8x + 112
5x = 60
Therefore x = 60/5 = 12
So box 1 contains 24 Green, 12 blue and 16 red pencils.
Total pencils in box 1 = 52
Box 2 contains 8 more than 7/13 of pencils in box 1.
= 8 + 7/13 (52)
= 36 pencils
Probability of selecting 1 red pencil = 1/3
So number of red pencils = 1/3 * 36 = 12
Green: Blue ratio = 1 : 2
Number of green pencil = 1/3 * (36-12) = 8
Number of blue pencil = 16
Box 3 contains Red pencils = Green + Blue Pencils in box 2 = 8 + 16 = 24
Green pencils = Green + Red pencils in pencil box 2 = 8 + 12 = 20
Probability of selecting a blue pencil = 3/14.
So number of blue pencil = x/ x + 44 = 3/14
14x = 3x + 132
11x = 132
Therefore x = 12 = blue pencils
Box 3 contains 24 red, 20 green and 12 blue pencils. So total is 56.
Now some green pencils are transferred from box 1 to box 3.
Let number transferred be G, so total becomes 56 + G.
Probability of blue pencil = 12 / 56+G = 3/16
192 = 168 + 3G
3G = 24
G = 8
So 8 Green Pencils are transferred from Box 1 to Box 3.
Number of remaining pencils in Box 1 = 52 - 8 = 44