A woman buys toffees at Rs $2.50$ a dozen and an equal number at Rs. $3$ a score. She sells them at Rs. $3.60$ a score and thus makes a profit of Rs. $10$ . How many toffees did she buy?

10000

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12000

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5000

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6000

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Solution

The correct option is B $12000$
Let woman buys 2x number of toffeees.

Then she buys x tofees at Rs 2.50 a dozen and x toffees at Rs 3 a score.

Hint : $1 d o z e n = 12 o b j e c t s a n d 1 s c o r e = 20 o b j e c t s$ .

$∴ T o t a l C P = (\frac{2.50}{12} \times x) + (\frac{3}{20} \times x) = \frac{5}{24} x + \frac{3}{20} x = \frac{43 x}{120}$

Now, she sells them at Rs $3.60$ a score.

$∴ T o t a l S P = \frac{3.60}{20} \times 2 x = \frac{9 x}{25}$

Since, it is given that she makes a profit of Rs $10$

$\Rightarrow S P - C P = 10$

$\Rightarrow \frac{9 x}{25} - \frac{43 x}{120} = 10$

$\Rightarrow \frac{216 x - 215 x}{600} = 10$

$\Rightarrow \frac{x}{600} = 10$

$∴ x = 6000$

Hence she buys $2 x = 2 \times 6000 = 12000 t o f f e e s$

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