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Basic Maths: Test 47
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Question 1 
$3.5\overline{625}$ is equal to
$3\frac{4394}{995}$
 
$3\frac{292}{333}$  
$3\frac{562}{999}$  
$3\frac{878}{999}$ 
Question 1 Explanation:
\[\begin{align}
& 3.5\overline{625}=\frac{3562535}{9990} \\
& =\frac{35590}{9990}=3\frac{562}{999} \\
\end{align}\]
Question 2 
$0.65\times 6.52\times 6.5\times 0.35+0.35\times 3.5$ is equal to
9  
90  
9.9  
0.9 
Question 2 Explanation:
Expression
$\begin{align} & 0.65\times 6.52\times 6.5\times 0.35+0.35\times 3.5 \\ & =0.65\times 0.65\times 102\times 0.65\times 0.35\times 10+0.35\times 0.35\times 10 \\ & =10\left( {{\left( 0.65 \right)}^{2}}2\times 0.65\times 0.35+{{\left( 0.35 \right)}^{2}} \right) \\ & =10{{\left( 0.650.35 \right)}^{2}} \\ & =10\times 0.09 \\ & =0.9 \\ \end{align}$
$\begin{align} & 0.65\times 6.52\times 6.5\times 0.35+0.35\times 3.5 \\ & =0.65\times 0.65\times 102\times 0.65\times 0.35\times 10+0.35\times 0.35\times 10 \\ & =10\left( {{\left( 0.65 \right)}^{2}}2\times 0.65\times 0.35+{{\left( 0.35 \right)}^{2}} \right) \\ & =10{{\left( 0.650.35 \right)}^{2}} \\ & =10\times 0.09 \\ & =0.9 \\ \end{align}$
Question 3 
$\frac{{{\left( 7.89 \right)}^{2}}{{\left( 4.56 \right)}^{2}}}{7.89+4.56}$
is simplified to
3.3
 
3.33  
3.23  
3.26 
Question 3 Explanation:
Let 7.89= a and 4.56 = b
Therefore expression
$\begin{align} & =\frac{{{a}^{2}}{{b}^{2}}}{a+b} \\ & =\frac{\left( ab \right)\left( a+b \right)}{a+b} \\ & =ab=7.894.56=3.33 \\ \end{align}$
Therefore expression
$\begin{align} & =\frac{{{a}^{2}}{{b}^{2}}}{a+b} \\ & =\frac{\left( ab \right)\left( a+b \right)}{a+b} \\ & =ab=7.894.56=3.33 \\ \end{align}$
Question 4 
A sum of Rs.27.15 is made of 170 coins which are either 10 paise coins of 25 paise coins. The number of 10 paise coins is:
119  
125  
109  
96

Question 4 Explanation:
Let the number of 10 paise coins be x
Number of 25 paise coins = 180  x
According to the question,
$\begin{align} & x\times 10+25\,\,\left( 170x \right) \\ & =27.15\times 100 \\ & \Rightarrow 10x+425025x=2715 \\ & \Rightarrow 15x=45002715=1785 \\ & \Rightarrow x=\frac{1785}{15}=119 \\ & \therefore \,\,Number\,\,\,of\,\,10\,\,paise\,\,coins\,\,\,=119 \\ \end{align}$
Number of 25 paise coins = 180  x
According to the question,
$\begin{align} & x\times 10+25\,\,\left( 170x \right) \\ & =27.15\times 100 \\ & \Rightarrow 10x+425025x=2715 \\ & \Rightarrow 15x=45002715=1785 \\ & \Rightarrow x=\frac{1785}{15}=119 \\ & \therefore \,\,Number\,\,\,of\,\,10\,\,paise\,\,coins\,\,\,=119 \\ \end{align}$
Question 5 
(25)^{3}Ã· (5)^{2 }=?
5  
625  
125
 
25 
Question 5 Explanation:
$?=\frac{25\times 25\times 25}{5\times 5}=625$
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