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Ask QuestionPosted by Harsh Khanpara 7 years, 7 months ago
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Posted by Srushti Kunkolienkar 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
Let the ten's digit of the required number be x and its unit's digit be y.
As per given condition
A two-digit number is four times the sum of its digits
Then, 10x + y = 4(x + y)
{tex}\Rightarrow{/tex} 6x - 3y = 0
{tex}\Rightarrow{/tex} 2x - y = 0......... (i)
And A two-digit number is twice the product of its digits.
Also, 10x + y = 2xy. ....... (ii)
Putting y = 2x from (i) in (ii), we get
10x + 2x = 4x2
{tex}\Rightarrow{/tex} 4x2- 12 x = 0
{tex} \Rightarrow{/tex} 4x(x - 3) = 0
{tex}\Rightarrow{/tex} x - 3 = 0
{tex}\Rightarrow{/tex} x = 3 [ten's digit, x {tex}\ne{/tex} 0]
Putting x = 3 in (i), we get y = 6.
Thus, ten's digit = 3 and unit's digit = 6.
Hence, the required number is 36.
Posted by Srushti Kunkolienkar 7 years, 7 months ago
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Posted by Prachi Ghosh 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
According to question It is given that in {tex}\triangle {/tex}ABC, AE is the bisector of the {tex}\angle CAD{/tex}.
Also, BE = BC + CE = 12 + x
CE= x, AB = 10, AC = 6
Since, We know that, the external bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
{tex}\therefore \frac { B E } { C E } = \frac { A B } { A C }{/tex}
{tex}\Rightarrow \frac { 12 + x } { x } = \frac { 10 } { 6 }{/tex}
{tex}\Rightarrow{/tex} 6(12 + x) = 10x
{tex}\Rightarrow{/tex} 72 + 6x = 10x
{tex}\Rightarrow{/tex} 4x = 72
{tex}\Rightarrow x = \frac { 72 } { 4 }{/tex}
= 18 cm
{tex}\Rightarrow{/tex} CE = 18 cm
Posted by Ujjwal Rajput Rajput 7 years, 7 months ago
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Sia ? 6 years, 4 months ago
If a and b are odd numbers then it should be in 2q+1 or 2q+3 form where q is a positive integer.
Let a = 2q + 3 , b = 2q + 1 and a > b
Now, {tex}\frac{a + b } {2} = \frac{ 2q + 3 + 2q + 1}{2}{/tex}
{tex}= \frac { 4 q + 4 } { 2 }{/tex}
= 2q + 2
{tex}\frac{a+b}{2}{/tex}=2(q+1) = an even number..........(1)
Now
{tex}\frac { a - b } { 2 } = \frac { ( 2 q + 3 ) - ( 2 q + 1 ) } { 2 }{/tex}
{tex}= \frac { 2 q + 3 - 2 q - 1 } { 2 }{/tex}
{tex}\frac{a-b}{2}= \frac { 2 } { 2 }{/tex} = 1 = an odd number..........(2)
Hence From (1) and (2) {tex}\frac{a+b}{2}{/tex} and {tex}\frac{a-b}{2}{/tex} are even and odd numbers respectively
Posted by Kirat Singh 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
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