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Basic Maths: Test 50
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Question 1 
A Washing Machine consumes 8 units of electricity in 30 minutes and a tube light, consumes 18 units of electricity in 6 hours, How much total unit of electricity will both Washing Machine and Tube light consume in 8 days if they run 10 hours a day?
1280 units  
1528 units  
1248 units  
1520 units 
Question 1 Explanation:
Total electric consumption = (10 Ã—16Ã—8+3Ã—10Ã—8) units
= (1280 +240) units = 1520 units
= (1280 +240) units = 1520 units
Question 2 
On Independence Day sweets were to be equally distributed among 400 children. But on that particular day, 100 children remained absent. Thus, each child got 3 sweets extra. How many sweets did each child get?
6
 
12  
9  
Cannot be determined 
Question 2 Explanation:
Number of sweets for 100 absent children = 300 Ã— 3 =900
Therefore Number of sweets each students gets = $\frac{900}{100}+3=12$
Therefore Number of sweets each students gets = $\frac{900}{100}+3=12$
Question 3 
There are some peacocks and some leopards in a forest. If the total number of animal heads in the forest are 858 and total number of animal legs are 1,746, what is the number of peacocks in the forest?
845  
833  
800  
None of these

Question 3 Explanation:
If the number of peacocks in the forest be x, then number of leopards = 858  x
Therefore
$\begin{align} & x\times 2+\left( 858x \right)\times 4=1746 \\ & \Rightarrow 2x=34321746=1686 \\ & \Rightarrow x=\frac{1686}{2}=843 \\ \end{align}$
Therefore
$\begin{align} & x\times 2+\left( 858x \right)\times 4=1746 \\ & \Rightarrow 2x=34321746=1686 \\ & \Rightarrow x=\frac{1686}{2}=843 \\ \end{align}$
Question 4 
$\frac{139\times 139+135\times 135+18765}{139\times 139\times 139135\times 135\times 135}$
is equal to
4
 
270  
$\frac{1}{4}$  
$\frac{1}{270}$ 
Question 4 Explanation:
$\begin{align}
& =\frac{139\times 139+135\times 135+18765}{139\times 139\times 139135\times 135\times 135} \\
& \left[ 139\times 135=18765 \right] \\
& Let\,139=a\,\,and\,\,135=b \\
& Therefore\,\,\,\exp ression\,\,=\frac{{{a}^{2}}+{{b}^{2}}+ab}{{{a}^{3}}+{{b}^{3}}} \\
& =\frac{{{a}^{2}}+{{b}^{2}}+ab}{\left( ab \right)\left( {{a}^{2}}+{{b}^{2}}+ab \right)} \\
& =\frac{1}{ab} \\
& =\frac{1}{139135} \\
& =\frac{1}{4} \\
\end{align}$
Question 5 
$\left( \frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+\frac{1}{17.19} \right)$
is equal to
6/133
 
2/133  
12/133  
1/133 
Question 5 Explanation:
\[\begin{align}
& \left( \frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+\frac{1}{17.19} \right) \\
& =\frac{1}{2}\left( \frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19} \right) \\
& =\frac{1}{2}\left( \frac{1}{7}\frac{1}{9}+\frac{1}{9}\frac{1}{11}+\frac{1}{11}\frac{1}{13}+\frac{1}{13}\frac{1}{15}+\frac{1}{15}\frac{1}{17}+\frac{1}{17}\frac{1}{19} \right) \\
& =\frac{1}{2}\left( \frac{1}{7}\frac{1}{19} \right) \\
& =\frac{1}{2}\left( \frac{197}{133} \right) \\
& =\frac{1}{2}\times \frac{12}{133} \\
& =\frac{6}{133} \\
\end{align}\]
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