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Yogita Ingle 6 years, 2 months ago
Let the digit at unit's place be x.
GIVEN : digit at Ten’s place = 3x
Number formed :
10 × 3x + x = 30x + x = 31x
Number formed after reversing the digits:
10 × x + 3(x )= 10x +3x = 13x
ATQ,
31x -54 = 13x [Given]
31x -13x = 54
18x = 54
x = 54/18
x= 3
Number = 31x = 31 × 3 = 93
Hence, the number is 93.
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Yogita Ingle 6 years, 2 months ago
For the points to be collinear , p = 4
Step-by-step explanation:
Given ,
Points = ( p+1 , 2p-2 ), ( p-1 , p) and (p-3 , 2p-6)
For the given points ( x₁ , y₁ ) , ( x₂ , y₂ ) and ( x₃ , y₃) to be collinear then
[ x₁ ( y₂ - y₃ ) + x₂( y₃ - y₁ )+ x₃( y₁- y₂ )] = 0
Here,
x₁ = p + 1 y₁ = 2p - 2
x₂ = p - 1 y₂ = p
x₃ = p - 3 y₃ = 2p - 6
Substituting the values in the formula ,
( p + 1 ) ( p - ( 2p - 6 ) ) + ( p - 1 ) ( 2p - 6 - ( 2p - 2 ) ) + ( p - 3 ) ( 2p - 2 - ( p ) ) = 0
( p + 1 ) ( p - 2p + 6 ) ) + ( p - 1 ) ( 2p - 6 - 2p + 2 ) ) + ( p - 3 ) ( 2p - 2 - p ) = 0
( p + 1 ) ( -p + 6 ) + ( p - 1 ) ( -4 ) + ( p - 3 ) ( p - 2 ) = 0
- p² - p + 6p + 6 - 4p + 4 + p² - 3p - 2p + 6 = 0
- 4p + 16 = 0
4p = 16
Dividing both the sides by 4
4p / 4 = 16 / 4
p = 4
Hence,
For the points to be collinear , p = 4
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Yogita Ingle 6 years, 2 months ago
\text {product of the two numbers }=L C M \times H C F
Therefore, the we can substitute the known values in the formula to get the values of "x"
{tex}\begin{array}{l}{x \times 18=36 \times 2} \\\\ {x=\frac{72}{18}} \\\\ {x=4}\end{array}{/tex}
Hence the value of unknown number "x" is 4
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Yogita Ingle 6 years, 2 months ago
HCF of any two consecutive natural numbers is 1. because the difference between two consecutive numbers is one & if the HCF is greater than one the the two consecutive numbers has to be divisible by that number which is not possible.
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Mr.Xxx ??? 6 years, 2 months ago
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