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09 Dec 2022, 12:15
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Packet X contains pens, pencils and erasers in the ratio 1:2:3. Packet Y contains pens and pencils in the ratio 4:5. If the total number of pens and pencils in both the packets combined is 13 and 20 respectively, what is the number of erasers in Packet X?
A. 5
B. 6
C. 15
D. 18
E. 20
A. 5
B. 6
C. 15
D. 18
E. 20
09 Dec 2022, 13:19
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Packet X has pens,pencils,erasers in ratios 1:2:3
Packet Y has pens, and pencils in ratios 4:5
Assume a is the common factor of ratios in Packet X, and b is the common factor of ratios in Packet Y.
For pens from packets X and Y, we have following equation:
a + 4b = 13 .... (1)
For pencils from packets X and Y, we have following equation:
2a + 5b = 20 ....(2)
Solving equations (1) and (2).....Subtracting (1) from (2)
a + b = 7 .... (3)
--> a = 7-b
putting vaue of a in (1): 7-b + 4b = 13 --> 3b = 6 --> b = 2
Putting b=2 in (3) ---> a = 5
We now have the common factors of the ratios in both boxes. The ratios of pens, pencils and erasers in Packet X are: 1:2:3
With the common factor of a=5, the ratios become: 5:10:15 ---> hence we have 15 erasers in Packet X
Packet Y has pens, and pencils in ratios 4:5
Assume a is the common factor of ratios in Packet X, and b is the common factor of ratios in Packet Y.
For pens from packets X and Y, we have following equation:
a + 4b = 13 .... (1)
For pencils from packets X and Y, we have following equation:
2a + 5b = 20 ....(2)
Solving equations (1) and (2).....Subtracting (1) from (2)
a + b = 7 .... (3)
--> a = 7-b
putting vaue of a in (1): 7-b + 4b = 13 --> 3b = 6 --> b = 2
Putting b=2 in (3) ---> a = 5
We now have the common factors of the ratios in both boxes. The ratios of pens, pencils and erasers in Packet X are: 1:2:3
With the common factor of a=5, the ratios become: 5:10:15 ---> hence we have 15 erasers in Packet X
12 Dec 2022, 14:38
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Given ratio X:
Pen : Pc : E
1: 2: 3
Given ratio Y:
Pen : Pc
4 : 5
Given information:
Final ratio Pen : Pc = 13 : 20
How many erasers?
I like to write down the ratio's underneath each other, for an easy multiplication, so
Pen X: 1
Pc X: 2
E X: 3
Pen Y: 4
Pc Y: 5
Ratio Y * 2 and ratio X * 5 gives:
Pen X: 5
Pc X: 10
E X: 15
Pen Y: 8
Pc Y: 10
Pen = 13
Pencil = 20
Eraser = 15
Final ratio: 13:20:15
Pen : Pc : E
1: 2: 3
Given ratio Y:
Pen : Pc
4 : 5
Given information:
Final ratio Pen : Pc = 13 : 20
How many erasers?
I like to write down the ratio's underneath each other, for an easy multiplication, so
Pen X: 1
Pc X: 2
E X: 3
Pen Y: 4
Pc Y: 5
Ratio Y * 2 and ratio X * 5 gives:
Pen X: 5
Pc X: 10
E X: 15
Pen Y: 8
Pc Y: 10
Pen = 13
Pencil = 20
Eraser = 15
Final ratio: 13:20:15
