A) Kusum buys some chocolates at the rate of Rs. 10 per chocolate. She also buys an equal number of candies at the rate of Rs. 5 per candy. She makes a 20% profit on chocolates and 8% profit on candies. At the end of the day, all chocolates and candies are sold out and her profit is Rs. 240. Therefore, Kusum buys 100 chocolates.
B) A carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charges are Rs. 200/hr. So, the carpenter will work for 7 hours.
C) On dividing Rs. 200 between A and B such that twice of A's share is less than 3 times B's share by 200. So, B's share is Rs. 120.
D) Madhulika thought of a number, double it and added 20 to it. On dividing the resulting number by 25, she gets 4. Hence, the required number is 45.
Correct Answer: D
Solution :
[a] Let the number of chocolates purchased be x. \[\therefore \]The number of candies purchased \[=\text{ }x\] Cost of \[x\] chocolates \[=\text{Rs}\text{. }10x\] and cost of \[x\] candies \[=\text{ Rs}\text{. }5x\] According to question, 20% of 10x + 8% of \[5x=\text{Rs}.240\] \[\Rightarrow \frac{20}{100}\times 10x+\frac{8}{100}\times 5x=240\] \[\Rightarrow \frac{200x+40x}{100}=240\Rightarrow 240x=24000\] \[\Rightarrow x=\frac{24000}{240}\Rightarrow x=100\] Hence, the number of chocolates purchased is 100. [b] Let the carpenter worked for \[x\]hours. \[\therefore \] Labour charges for \[x\] hours \[=\text{ Rs}\text{. }200x\] According to question. \[200x+1100=2500\] \[\Rightarrow 200x=2500-1100\Rightarrow 200x=1400\] \[\Rightarrow x=\frac{1400}{200}\Rightarrow x=7\] Hence, the carpenter worked for 7 hours. [c] Let B's share be \[\text{Rs}\text{. }x\]. Since, \[2\text{ }\times \] A?s share \[=3\times \]B's share - 200 \[\Rightarrow A's\]share \[=\frac{3x-200}{2}\] According to question, \[\frac{3x-200}{2}+x=200\] \[\Rightarrow \frac{3x}{2}-\frac{200}{2}+x=200\Rightarrow \frac{3x}{2}-100+x=200\] \[\Rightarrow \frac{3x}{2}+x=200+100\Rightarrow \frac{3x+2x}{2}=300\] \[\Rightarrow \frac{5x}{2}=300\Rightarrow x=\frac{2x300}{5}\Rightarrow x=120\] Therefore, B's share \[\text{=Rs}\text{.}\,\,\text{120}\] [d] Let the number be \[x\]. Double the number and added 20 to it, we get 2x + 20 According to the question, \[\frac{1}{25}(2x+20)=4\] \[\Rightarrow 2x+20=4\times 25\Rightarrow 2x+2=100\] \[\Rightarrow 2x=100-20\to 2x=80\] \[\Rightarrow x=\frac{80}{2}\Rightarrow x=40\]
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