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Q.

I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which is half more than what I had paid. What percent of the total amount paid by me was paid for the pens?

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a

37.5 %

b

62.5 %

c

50 %

d

None of these

answer is B.

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Detailed Solution

Concept: Assigning the variables for total amount, cost, pen, pencil, and eraser allows us to begin solving the issue. Then, under the presumption that we purchased 5 pens, 7 pencils, and 4 erasers, we write our first equation. We next use Rajan's purchase of 6 pens, 8 erasers, and 14 pencils for a price that is

50 %

higher than our own to create our second equation. We may calculate the entire cost of a pen using these two formulae. The percentage of "y" in

"x" = \frac{y}{x} \times 100

is then used to calculate the percentage of the price we paid for the pens.
Rajan purchased 6 pens, 8 erasers, and 14 pencils in addition to the 5 pens, 7 pencils, and 4 erasers we purchased. He made a payment that was 50% greater than what I had made. The percentage of the total cost that we spent on pens must be determined.
Assume that our entire outlay is "A" and that the cost of pens, pencils, and erasers is "p," "s," and "e."
Paying the sum "A," we purchased 5 pens, 7 pencils, and 4 erasers.
Thus, we have

5 p + 7 s + 4 e = A . (1) .

The issue states that Rajan paid

50 %

more than we did. Rajan therefore spent

(1 + \frac{1}{2}) A = \frac{3}{2} A

and purchased

6 pens, 8 erasers, and 14 pencils 32 A

is the amount.
So, we get

6 p + 14 s + 8 e = \frac{3}{2} A

\Rightarrow 10 p + 14 s + 8 e - 4 p = \frac{3}{2} A \Rightarrow 2 (5 p + 7 s + 4 e) - 4 p = \frac{3}{2} A From equation (1) we get, \Rightarrow 2 A - 4 p = \frac{3}{2} A

\Rightarrow 2 A - \frac{3}{2} A = 4 p

⇒

\frac{1}{2}

A=4p
⇒p=

\frac{1}{8}

A
Therefore, each pen costs

\frac{1}{8}

A.
Let's calculate the price of 5 pens.
Because 5p=5, we have to pay for 5 pens (

\frac{1}{8}

A) .
5p=5A8.
However, we have already paid A in total.
Let's calculate the proportion of

\frac{5}{8}

A in A.
We are aware that

\frac{Y}{X}

×100 is used to calculate the percentage of y in x.
As a result, we get

\frac{5}{8} \times \frac{A}{A} \times 100

as the proportion of

\frac{5}{8}

A in A.
⇒

\frac{5}{8}

×100=5×12.5=62.5.
Therefore, we have already paid

62.5 percent

of the total cost of the pens.
Hence, the answer is option (2) .
ExamType: CBSE

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