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Basic Maths: Test 48

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Question 1
${{\left( 729 \right)}^{0.31}}\times {{\left( 27 \right)}^{0.15}}$ is equal to
A
9
B
27
C
243
D
27.243
Question 1 Explanation: 
$\begin{align} & ={{\left( 729 \right)}^{0.31}}\times {{\left( 27 \right)}^{0.15}} \\ & ={{\left( {{3}^{5}} \right)}^{0.31}}\times {{\left( {{3}^{3}} \right)}^{0.15}} \\ & ={{\left( 3 \right)}^{5\times 0.31}}\times {{\left( 3 \right)}^{3\times 0.15}} \\ & ={{\left( 3 \right)}^{1.55}}\times {{\left( 3 \right)}^{0.45}}={{\left( 3 \right)}^{1.55+0.45}} \\ & ={{\left( 3 \right)}^{2}}=9 \\ \end{align}$
Question 2
$\left( \frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17} \right)$ is equal to
A
$\frac{17}{16}$
B
$\frac{4}{17}$
C
$\frac{7}{17}$
D
$\frac{16}{17}$
Question 2 Explanation: 
$\begin{align} & =\left( \frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17} \right) \\ & =\frac{1}{4}\left[ \left( \frac{4}{1\times 5} \right)+\left( \frac{4}{5\times 9} \right)+\left( \frac{4}{9\times 13} \right)+\left( \frac{4}{13\times 17} \right) \right] \\ & =\frac{1}{4}\left[ \left( 1-\frac{1}{5} \right)+\left( \frac{1}{5}-\frac{1}{9} \right)+\left( \frac{1}{9}-\frac{1}{13} \right)+\left( \frac{1}{13}-\frac{1}{17} \right) \right] \\ & =\frac{1}{4}\left( 1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17} \right) \\ & =\frac{1}{4}\left( 1-\frac{1}{17} \right)=\frac{1}{4}\left( \frac{17-1}{17} \right) \\ & =\frac{1}{4}\times \frac{16}{17}=\frac{4}{17} \\ \end{align}$
Question 3
$0\overline{.158263}\div 0\overline{.316526}$ is equal to
A
10
B
2
C
$\frac{1}{2}$
D
$\frac{1}{3}$
Question 3 Explanation: 
$\begin{align} & =0\overline{.158263}\div 0\overline{.316526} \\ & =\frac{158263}{999999}\div \frac{316526}{999999} \\ & =\frac{158263}{316526}=\frac{1}{2} \\ \end{align}$
Question 4
The cost of 9 kg of apples is Rs.450. The cost of 16 dozen mangoes is Rs.432 and the cost of 6 kg of oranges is Rs.240. What is the total cost of 8 kg of apples, 8 dozens of mangoes and, 8 kg of oranges?
A
Rs.900
B
Rs.980
C
Rs.1000
D
Rs.936
Question 4 Explanation: 
$\begin{align} & \operatorname{Cos}t\,\,\,of\,\,8kg\,\,\,of\,apples\, \\ & =\frac{450}{9}\times 8=rs.400 \\ & \operatorname{Cos}t\,\,of\,\,8\,dozens\,\,of\,\,mangoes\, \\ & =\frac{432}{16}\times 8=Rs.216 \\ & \operatorname{Cos}t\,\,of\,\,8kg\,\,of\,\,oranges \\ & =\frac{240}{6}\times 8=Rs.320 \\ & Therefore\,\,Total\,\,\,\cos t\,=Rs.\,\left( 400+216+320 \right) \\ & =Rs.936 \\ \end{align}$
Question 5
Reena's monthly income is equal to the cost of 34kg of nuts. Cost of 10kg of nuts is equal to the cost of 20 kgs of apples. If cost of 12 kg of apples is Rs.1500, what is Reena's annual salary? (At some places annual income and at some place monthly income are given)
A
Rs.1 lac 20 thousand
B
Rs.1 lac 2 thousand
C
Rs.2 lacs 20 thousand
D
Cannot be determined
Question 5 Explanation: 
$\begin{align} & \because \,\,\,\,12\,kg\,\,\,\,of\,\,\,apples=Rs.1500 \\ & 20\,kg\,\,of\,\,apples\,=\frac{1500}{12}\times 20 \\ & =Rs.\,2500 \\ & 10\,\,kg\,\,\,of\,\,nuts\,\,=Rs.\,2500 \\ & 34\,\,kg\,\,\,of\,\,nuts\,\,=\frac{2500}{10}\times 34=Rs.8500 \\ & Reena's\,\,\,monthly\,\,\,income \\ & =Rs.\,\,8500 \\ & Reena's\,\,\,annual\,\,income \\ & =Rs.\,\left( 12\times 8500 \right) \\ & =Rs.\,1\,lac\,\,2\,\,thousand \\ \end{align}$
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