In arithmetical reasoning, questions are based on calculations on problems, data based, ages, Venn-diagrams. This is to test the ability of candidate and the candidate is required to select the appropriate answer for the given questions.

Arithmetical reasoning questions are divided into four types. They are:
1. Calculations based on problems.
2. Data based questions.
3. Problems on ages.
4. Venn diagram based questions.

Given that,
W, X, Y, Z play a game of cards.
Let
X + 6 = Y -------(i)
W - 3 = Y - 6 -------(ii)
W + 3 = 2Z -------(iii)
X + Z = 50 -------(iv)
Place Y = W + 3 from (ii) into (i)
X + 6 = W + 3
W - X = 3 -------(v)
Place Z = 50 - X from (iv) into (iii),
W + 3 = 2Z
W + 3 = 2(50 - X)
W + 3 = 100 - 2X
W + 2X = 97 -------(vi)
By solving (v) and (vi),
X = [latex]\frac{94}{3}[/latex] and W = [latex]\frac{106}{3}[/latex] = 35.3 ≅ 35
Therefore, W has approximately 35 cards.

1. Students failed in four or less subjects = students failed in only 1 subject + students failed in only 2 subjects + students failed in only 3 subjects + students failed in only 4 subjects
= students failed in only 1 subject + students passed in only 3 subjects + students passed in only 2 subjects + students passed in only 1 subject
= (70 + 200 + 140 + 150 + 220) + 1500 + 1200 + 800
= 4280
2. Students failed in all the subjects = students appeared - (students passed in 1, 2, 3 or 5 subjects + students failed in 1 subject only)
= 10000 - (5000 + 1500 + 1200 + 800 + 70 + 200 + 140 + 150 + 220)
= 10000 - 9280
= 720

Let George's present age be [latex]x[/latex] years.
Then, John's present age = 2[latex]x[/latex] years.
Three years ago, George's age = ([latex]x[/latex] - 3) years.
John's age = (2[latex]x[/latex] - 3) years.
Now,
(2[latex]x[/latex] - 3) = 3([latex]x[/latex] - 3)
⇒ 2[latex]x[/latex] - 3 = 3[latex]x[/latex] - 9
⇒ [latex]x[/latex] = 6
Therefore, John's present age = 2[latex]x[/latex] = 12 years.

Number of students who failed in at least two subjects = number of candidates who failed in two or more subjects = (10 + 12 + 12 + 5) = 39
Therefore, Required percentage = ([latex]\frac{39}{500}[/latex] x 100 )% = 7.8%

Let
The number of questions attempted correctly be [latex]x[/latex]
Then, number of incorrect ones = 80 - [latex]x[/latex]
Therefore, 4[latex]x[/latex] - 1(60 - [latex]x[/latex]) = 140
⇒ 5[latex]x[/latex] = 200
⇒ [latex]x[/latex] = [latex]\frac{200}{5}[/latex]
⇒ [latex]x[/latex] = 40
Therefore, the number of questions he attempts correctly = 40.

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