Latest 3i-Infotech Aptitude Question SOLUTION: Q. An Eraser, Pencil, Notebook together costs $1.00. Notebook costs more than the cost of 2 Pencils. 3 Pencil costs more than 4 Erasers. 3 Erasers costs more than a Notebook. How m

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Q. An Eraser, Pencil, Notebook together costs $1.00. Notebook costs more than the cost of 2 Pencils. 3 Pencil costs more than 4 Erasers. 3 Erasers costs more than a Notebook. How much does a pencil costs?

Asked In 3i-Infotech chandreyee chowdhury (10 years ago)

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Read Solution (1) :

Mohiuddin Khokan  (9 years ago)

Given:
P + E + N = 100 cents

N > 2 P
3 P > 4 E
3 E > N

3 P > 4 E → 2 P > 8/3 E
N > 2 P → N > 8/3 E
N < 3 E (given)
Therefore: 8/3 E < N < 3 E

3P > 4 E → P > 4/3 E
2P < N → P < N/2
N < 3 E → N/2 < 3/2 E
Therefore: 4/3 E < P < 3/2 E

Converting those to sixths, we have
16/6 E < N < 18/6 E or N = roughly 17 / 6 E
8/6 E < P < 9/6 E or P = roughly 8.5 / 6 E

Now try some values for E:
E P N Total
6 8.5 17 31.5
12 17 34 63
18 25.5 51 94.5
That's close to 100, so with a bit of fiddling, we can make it:
E = 19 P = 26 N = 55 Total = 100

Checking the conditions:
N > 2 P ? ... 55 > 2 * 26 ? ... .. 55 > 52 ... yes
3 P > 4 E ? . 3 * 26 > 4 * 19 ? . 78 > 76 .. yes
3 E > N ? ... 3 * 19 > 55 ? ... .. 57 > 55 ... yes

Answer:
Eraser: 19 cents
Pencil: 26 cents
Notebook: 55 cents

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