Question

a shopkeeper earns a profit of rs 5 by selling a notebook and incurs a loss of 50 paise per pencil and eraser while selling these from old stock on a particular day she earns a profit of 30 . If she sold 10 notebooks and the numbers of pencil and erasers she sold are in the ratio 6:4 find the number of pencil and eraser sold on that day​

Answer 1

Answer:

• PENCILS SOLD = 24
• ERASERS SOLD = 16

Solution:

Given that, the shopkeeper earns Rs 5 by selling a notebook and incurs a loss of Rs 0.5 ( 50 paisa as 1 rupees = 100 paise ) per eraser and pencil.

On a particular day, she sold 10 notebooks, and the ratio of numbers of eraser to numbers of pencil sold was 6:4 and earned a profit of Rs 30.

Let's first find the profit made by selling those 10 notebooks. Since, 1 notebook earns her a profit of Rs 5. Then selling 10 notebooks will earn her...

> Profit of 1 notebook × 10

> 5 × 10

> 50 Rupees.

Now, it's easier to find the loss, which is equal to...

> Profit earned by 10 notebooks - Final profit earned

> 50 - 30

> Rs 20

Which means, she lost Rs 20 by selling the erasers and pencil. Now, 1 eraser and 1 pencil loses her Rs 0.5

From the ratio, Let the number of pencils be 6k and number of erasers be 4k ( k = common factor )

> Loss = Loss for selling '6k' pencils + Loss for selling '4k' erasers

> Loss = ( Number of pencils × Loss per pencil ) + ( Number of erasers × Loss per eraser )

> 20 = 6k × 0.5 + 4k × 0.5

> 20 = 3k + 2k

> 20 = 5k

> k = 4

Hence,

• Pencils sold = 6k = 6×4 = 24
• Erasers sold = 4k = 4×4 = 16

Answer 2

Answer:

• No. of pencils sold = 24
• No. of erasers sold = 16

Explanation:

Given information,

◐ A shopkeeper earns a profit of Rs 5 by selling a notebook and incurs a loss of 50 paise per pencil and eraser while selling these from old stock on a particular day she earns a profit of Rs 30.

◐ If she sold 10 notebooks and the numbers of pencil and erasers she sold are in the ratio 6:4 find the number of pencil and eraser sold on that day.

• Profit made by selling one notebook = Rs 10
• Loss on per pencil & eraser = 50 paise
• Final profit of that day = Rs 30
• No. of notebooks sold = 10
• Ratio of no. of pencils & erasers sold = 6:4
• No. of pencils sold = ?
• No. of erasers sold = ?

★ Profit earned by selling 10 notebooks :-

➻ Profit on one notebook × 10

➻ 5 × 10

➻ 50

• Hence, profit earned by selling 10 notebooks is Rs 50.

★ Loss on that day :-

➻ Profit on 10 notebooks - Final profit

➻ 50 - 30

➻ 20

• Hence, loss made by by selling pencils and erasers on that day is Rs 20.

★ Loss per one pencil & one eraser in Rs :-

✪ One Rs = 100 paise ✪

➻ Loss in Rs = 50/100

➻ Loss in Rs = Rs 0.5

• So, Loss per one pencil & one eraser is Rs 0.5.

Let,

• Number of pencils & erasers sold = 6x & 4x

Now,

➻ Loss on that day = Loss on one pencil + Loss on one eraser

➻ Loss on that day = No. of pencils sold × Loss per pencil + No. of erasers sold × Loss per eraser

➻ 20 = 6x × 0.5 + 4x × 0.5

➻ 20 = 3x + 2x

➻ 20 = 5x

➻ x = 20/5

➻ x = 4

So,

◒ No. of pencils sold = 6x

◒ No. of pencils sold = 6 × 4

◒ No. of pencils sold = 24

Also,

◒ No. of erasers sold = 4x

◒ No. of erasers sold = 4 × 4

◒ No. of erasers sold = 16

• Hence, number of pencils and erasers sold on that day are 24 and 16.

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