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A scanner costs ₹7,000 less than a printer. If the cost of the printer is twice the cost of the scanner, then the cost of the scanner is:
₹6,000
₹14,000
₹7,000
₹7,500
₹7,000
Since the printer is twice the cost, the difference between them is exactly equal to the scanner's price. Therefore, the scanner cost is directly ₹7,000.
Scanner cost (S) = Printer cost (P) - 7000; Printer cost (P) = 2 * Scanner cost (S).
P=2S, S=P−7000
Since the printer is twice the cost, the difference between them is exactly equal to the scanner's price. Therefore, the scanner cost is directly ₹7,000.
Many students try to find the printer's price first and forget that the question asks specifically for the scanner's cost.
Define Variables
Let the cost of the scanner be S and the cost of the printer be P.
S,P
Formulate Equations
From the problem statement, we have two conditions: (1) S=P−7000 and (2) P=2S.
P=2S
Solve for S
Substitute the second equation into the first: S=(2S)−7000. Rearranging the terms, we get 7000=2S−S.
S=7000
C is correct because the substitution of the equations reveals that the cost of the scanner S is exactly ₹7,000.
This type of simple algebraic relation is foundational for more complex profit-loss and ratio-proportion word problems found in competitive exams.
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