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CAT 2019 Slot 1 — QA Question 22

Percentage ChangeEasy

On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the book at 10% gain, he gains Rs. 13. What is the cost price of the book in Rupees?

Answer & solution

Correct answer: 80

  • A

    95

  • B

    85

  • C

    100

  • 80

Solution

Easy

Profit/loss is on cost price, so work in cost prices. Scale them to 100p100p (pen) and 100b100b (book) so percentages give whole numbers. Each selling scenario gives one linear equation in pp and bb; solve the pair for bb.

1

First scenario. Pen at 5%5\% loss, book at 15%15\% gain, net gain 77.

95p+115b=(100p+100b)+7⇒ 15b−5p=7(1)\begin{aligned} &95p+115b=(100p+100b)+7\\ &\Rightarrow\ 15b-5p=7 \quad\text{(1)} \end{aligned}
2

Second scenario. Pen at 5%5\% gain, book at 10%10\% gain, net gain 1313.

105p+110b=(100p+100b)+13⇒ 10b+5p=13(2)\begin{aligned} &105p+110b=(100p+100b)+13\\ &\Rightarrow\ 10b+5p=13 \quad\text{(2)} \end{aligned}
3

Add to eliminate pp. Equations (1) and (2) have opposite 5p5p terms.

(15b−5p)+(10b+5p)=7+13[(1)+(2)]⇒ 25b=20⇒ b=45\begin{aligned} &(15b-5p)+(10b+5p)=7+13\quad\text{[(1)+(2)]}\\ &\Rightarrow\ 25b=20\\ &\Rightarrow\ b=\tfrac{4}{5} \end{aligned}
4

Cost price of the book. Recall it was scaled to 100b100b.

100b=100×45=80\begin{aligned} &100b=100\times\tfrac{4}{5}=80 \end{aligned}
Cost price of the book=Rs. 80\text{Cost price of the book}=\text{Rs. }80

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CAT 2019 Slot 1 QA Q22: On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the — Solution | TheCATExam