(a) A shop owner marked a shirt at a price to enable him to make a gain of 20%. During a special sales period, the shirt was sold at 10% reduction to a cust...
Question 1 Report
(a) A shop owner marked a shirt at a price to enable him to make a gain of 20%. During a special sales period, the shirt was sold at 10% reduction to a customer at N864.00. What was the original cost to the shop owner?
(b) A rectangular lawn of length (x + 5) metres is (x - 2) metres wide. If the diagonal is (x + 6) metres, find ;
(i) the value of x ; (ii) the area of lawn.
Answer Details
(a) Let the cost price be \(C\). Marked to gain \(20\%\): marked \(=1.2C\). Sold at \(10\%\) reduction: \[0.9\times1.2C=1.08C=864\Rightarrow C=\frac{864}{1.08}=\text{N}800.\] The original cost was N800.
(b) Length \((x+5)\), width \((x-2)\), diagonal \((x+6)\). By Pythagoras: \[(x+5)^{2}+(x-2)^{2}=(x+6)^{2}.\] \[x^{2}+10x+25+x^{2}-4x+4=x^{2}+12x+36\Rightarrow x^{2}-6x-7=0\Rightarrow(x-7)(x+1)=0.\] Taking the positive value, \(x=7\).
(ii) Area \(=(x+5)(x-2)=12\times5=60\text{ m}^{2}.\)
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