Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 8 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 1 and Q = 7
The required number is = 17
Let number of hit shots be 'X'
Let number of miss shots be 'Y'
Given X + Y = 40....(1)
50X - 10Y = 500.....(2)
Solving 1 and 2, we get
X = 15 and Y = 25
Therefore, number of hits = 15
This is a quadratic equation. To find n we multiply the last terms in each bracket together (2 times -5) = -10
To find ?a? we multiply the first terms in each bracket together (3x times 2x) = 6x2, So a = 6.
Thus a - n = 16
To find k we multiply the first term in the first bracket by the second term in the second bracket and add the result to the product of the second term in the first bracket and the first term in the second. (-15x + 4x) = -11x. So k = -11
16 - 11 = 5
Let the ten's digit be x and unit's digit be y. Then, (10x + y) - (x + y) = 9 or x = 1.
From this data we cannot find y, the unit's digit. So the data is inadequate..
Let the fraction be x/y. Then, x /(y+1) = 1/2
=> 2x - y = 1 ..........(i)and
(x + 1) / y = 1 => x - y = 1 .......(ii)
Solving (i) and (ii), we get : x = 2, y = 3. Hence, the required fraction is 2/3..
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