44. Find the mode of the data: (a) 8, 6, 2, 5, 6, 9, 13, 6, 4, 6
Answers
Answer:
G I V E N :
Abha bought 2 calculators at Rs 900. She sold one at profit of 20% and other at a loss of 20%. If the SP of both calculator was same, then find the CP of each calculator.
S O L U T I O N :
Let us assume the Cost Price of the Calculator be a
As the cost of both the calculators is ₹900
Thereby, Cost of the other calculator be 900 - a
Here, we will assume 100% as a point like zero
Now, as the first calculator suffered a loss of 20%
So, it should be 100% - 20% = 80%
\begin{gathered} \sf Selling \: Price \: of \: the \: calculator = \frak{a \times 80\%} \\ \\ \sf Selling \: Price = \frak{a \times \frac{80}{100} } \implies {\frak{ \frac{80}{100}a}} \implies \frak{ \green{ \frac{8}{10}a }}\end{gathered}
SellingPriceofthecalculator=a×80%
SellingPrice=a×
100
80
⟹
100
80
a⟹
10
8
a
Now, for the another calculator
It gained a profit of 20%
\begin{gathered} \sf Selling \: Price \: of \: another \: calculator = \frak{a \times 120\%} \\ \\ \sf Selling \: Price = \frak{a \times \frac{120}{100} } \implies {\frak{ \frac{120}{100}a}} \implies \frak{ \purple{\frac{12}{10}(900 - a)}}\end{gathered}
SellingPriceofanothercalculator=a×120%
SellingPrice=a×
100
120
⟹
100
120
a⟹
10
12
(900−a)
Now, a clue is provided that Selling Price of both the calculator are same
\begin{gathered} \sf Selling \: Price \: of \: first \: calculator = Selling \: Price \: of \: the \: other \: one \\ \\ \rightharpoonup\frak{ \frac{8}{10}a = \frac{12}{10}(900 - a)} \\ \\ \rightharpoonup \frak{ \frac{8}{10}a \times \frac{10}{12} = 900 - a } \\ \\ \rightharpoonup \frak{ \frac{8}{12}a = 900 - a } \\ \\ \rightharpoonup \frak{ \frac{2}{3}a = 900 - a } \\ \\ \rightharpoonup\frak{2a = 3(900 - a)} \\ \\ \rightharpoonup\frak{2a = 2700 - 3a} \\ \\ \rightharpoonup\frak{5a = 2700} \\ \\ \rightharpoonup\frak{a = \frac{2700}{5} } \\ \\ \rightharpoonup\frak{a = \cancel\frac{2700}{5} } \\ \\ \star \quad \underline{ \boxed{ \frak{a = 540}}}\end{gathered}
SellingPriceoffirstcalculator=SellingPriceoftheotherone
⇀
10
8
a=
10
12
(900−a)
Answer:
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!