CAT 2022 Arithmetic: Profit and Loss Test-4

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Arithmetic: Profit and Loss Test-4

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Question 1

A trader sells 145 metres of cloth for Rs.12, 325 at the profit of Rs.10 per metre of cloth. What is the cost price of 1 metre of cloth?

A	Rs.65
B	Rs.75
C	Rs.95
D	Rs.85

Question 1 Explanation:

Cost price of 145m long cloth
= Rs. (12325 – 145 x 10)
= Rs. 10875
Therefore cost price of 1 meter long cloth
10875/145 = Rs. 75

Question 2

Kamya purchased an item of Rs.46000 and sold it at a loss of 12 percent. With that amount she purchased another item and sold it at a gain of 12 percent. What was her overall gain/loss?

A	Loss of Rs.662.40
B	Profit of Rs.662.40
C	Loss of Rs.642.80
D	Profit of Rs.642.80

Question 2 Explanation:

$ \displaystyle \begin{array}{l}First\,\,\,S.P.=\frac{46000\times 88}{100}\\=Rs.40480\\Second\,\,S.P.=\frac{40480\times 112}{100}\\=Rs.\,45337.6\\\therefore \,\,\,Loss=Rs.\,\left( 46000-45337.6 \right)\\=Rs.662.4\end{array}$

Question 3

Rajni purchased a mobile phone and a refrigerator for Rs.12, 000 and Rs.10, 000 respectively. She sold the refrigerator at a loss of 12 per cent and mobile phone at a profit of 8 per cent. What is her overall loss/profit?

A	Loss of Rs.280
B	Profit of Rs.2,160
C	Loss of Rs.240
D	Profit of Rs.2, 060

Question 3 Explanation:

$ \displaystyle \begin{array}{l}Total\,\,\,CP\\=Rs.\,\left( 12000+10000 \right)\\=Rs.\,22000\\Total\,\,S.P\\=Rs.\,\left( \frac{12000\times 108}{100}+\frac{10000\times 88}{100} \right)\\=Rs.\,\left( 12960+8800 \right)\\=Rs.\,21760\\\therefore \,\,\,Loss=Rs.\left( 22000-21760 \right)\\=Rs.\,240\end{array}$

Question 4

A shopkeeper bought 30 kg of wheat at the rate of Rs.45 per kg. He sold forty percent of the total quantity at the rate of Rs.50 per kg. Approximately, at what price per kg, should he sell the remaining quantity to make 25 per cent overall profit?

A	Rs.54
B	Rs.52
C	Rs.50
D	Rs.60

Question 4 Explanation:

Cost price of 30 kg of wheat = 30 × 45= Rs. 1350
Total SP for an overall profit of
25% = (1350 x 125)/100 = Rs. 1687.5
Selling Price of 12 kg of Wheat = 12 x 50 = Rs. 600
Expected SP of 18kg of remaining wheat
$ \displaystyle =1687.5-600=Rs.1087.5$
Required selling price per kg
$ \displaystyle =\frac{1087.5}{18}=Rs.60$

Question 5

A watch is sold at a profit of 20%. If both the cost price and the selling price of the watch are decreased by Rs.100, the profit would be 5%more. Original cost price of the watch is

A	Rs.450
B	Rs.500
C	Rs.550
D	Rs.600

Question 5 Explanation:

Let the CP of the watch be Rs. x
$ \displaystyle \begin{array}{l}\therefore \,\,\,First\,\,\,SP=\frac{120x}{100}=Rs.\frac{6x}{5}\\Case\,II,\\CP=Rs.\left( x-100 \right)\\SP=Rs.\left( \frac{6x}{5}-100 \right)\\\Pr ofit=\left( \frac{6x}{5}-x \right)=Rs.\frac{x}{5}\\\therefore \,\,\frac{\frac{x}{5}}{x-100}\times 100=25\\\Rightarrow 25x-2500=20x\\\Rightarrow 5x=2500\\\Rightarrow x=\frac{2500}{5}=Rs.500\end{array}$

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