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Arithmetic Based DI

Master Arithmetic Data Interpretation. These are high-level sets where the graph is just a wrapper for deep arithmetic concepts like Time & Work, Probability, TSD, and Mensuration.

Model 1: Concept Bridging & Variable Handling

      <ul class='list-disc pl-6'>
        <li><strong>The Concept:</strong> Determine hidden variables first. Graphs often give relations (e.g., A is 20% more efficient than B) rather than direct values.</li>
        <li><strong>Variable Strategy:</strong> If data says 'x' men do work in 'y' days, and graph gives 'x-2' men take 'y+4' days, set up the M1D1 = M2D2 equation immediately.</li>
        <li><strong>Chain Rule (M1D1):</strong> Formula: (M1 ├Ч D1 ├Ч H1) / W1 = (M2 ├Ч D2 ├Ч H2) / W2. <br> (Where M = Men, D = Days, H = Hours per day, W = Work done).</li>
        <li><strong>Probability DI:</strong> When balls are 'x' and 'y', look for a probability statement (e.g., P(Red) = 1/3) to solve for variables before touching the questions.</li>
      </ul>

Example:

Q: Bag has x Red, 5 Blue. P(Red) = 1/3. Find x.
Solution: x / (x+5) = 1/3 -> 3x = x+5 -> 2x = 5 -> x=2.5 (Impossible? Check usually integer logic).

Model 2: Time, Speed, Distance (Circular Races)

      <ul class='list-disc pl-6'>
        <li><strong>Circular Track:</strong> Meeting at starting point = LCM of time taken by each.</li>
        <li><strong>Meeting anywhere:</strong> Relative Speed (Same dir = S1-S2, Opp dir = S1+S2). Time = Distance / Rel. Speed.</li>
        <li><strong>Number of distinct meeting points:</strong> Ratio of speeds a:b (reduced). Distinct points = |a-b| (same dir) or a+b (opp dir).</li>
      </ul>

Example:

Q: A speeds 20m/s, B speeds 30m/s on 600m track (Opposite). When meet at start?
Solution: Time A = 600/20=30s. Time B = 600/30=20s. LCM(30,20) = 60s.

Model 3: Mensuration (Melting & Molding)

      <ul class='list-disc pl-6'>
        <li><strong>Rule:</strong> When shape changes (melted/recast), VOLUME REMAINS CONSTANT.</li>
        <li><strong>Formulas:</strong> Cyl = ╧Аr┬▓h, Cone = (1/3)╧Аr┬▓h, Sphere = (4/3)╧Аr┬│.</li>
        <li><strong>n items:</strong> Total Vol = n ├Ч Vol of 1 small item.</li>
      </ul>

Example:

Q: Sphere r=10 melted into cones r=5, h=5? How many?
Solution: n = Vol(Sphere) / Vol(Cone).