4.5 Arithmetic-based DI (Profit-Loss, Time-Work, TSD) & Funnel/Scatter DI

4.5 Arithmetic-based DI (Profit-Loss, Time-Work, TSD) & Funnel/Scatter DI

Arithmetic-based Data Interpretation is the premier challenge of SBI PO Mains. These sets combine core arithmetic concepts—Profit, Loss & Discount, Time & Work, Time, Speed & Distance (TSD), and Simple/Compound Interest—with complex graphical formats such as tables, Funnel Charts, and Scatter Plots.

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1. Profit, Loss & Discount DI Mechanics

Profit-Loss DI sets present financial product data across columns representing Cost Price (CP), Marked Price (MP), Selling Price (SP), Discount Percentage, and Profit/Loss Percentage.

  Cost Price (CP) ----[ Markup % ]----> Marked Price (MP)
        |                                      |
        |                                [ Discount % ]
        v                                      v
  [ Profit / Loss % ] ----------------> Selling Price (SP)

Core Formulas for Chart Derivations

$\text{Marked Price (MP)} = \text{CP} \times \left( 1 + \frac{\text{Markup \%}}{100} \right)$ $\text{Selling Price (SP)} = \text{MP} \times \left( 1 - \frac{\text{Discount \%}}{100} \right)$ $\text{Profit} = \text{SP} - \text{CP} = \text{CP} \times \left( \frac{\text{Profit \%}}{100} \right)$ $\text{Discount Amount} = \text{MP} - \text{SP} = \text{MP} \times \left( \frac{\text{Discount \%}}{100} \right)$

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2. Time & Work DI Mechanics

Time & Work DI tables specify the number of days individual workers or pipes require to complete tasks. You must convert these time values into daily efficiency rates.

$\text{Work Rate (Efficiency)} = \frac{1}{\text{Time (Days)}}$ $\text{Total Work} = \text{LCM of individual completion times (in units)}$ $\text{Combined Rate (A + B)} = \frac{1}{T_A} + \frac{1}{T_B} = \frac{T_A + T_B}{T_A \times T_B}$

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3. Modern Visual Formats: Funnel Charts & Scatter Plots

Funnel Charts (Conversion Pipelines)

Funnel charts track customer progression through sequential process stages (e.g., Banking App Funnel: Downloads $\to$ Registrations $\to$ KYC Verification $\to$ Account Opened).

Stage 1: App Downloads [ 100,000 ] ------------------------------ (100% Base)
Stage 2: Registrations [  60,000 ] ------------ (60% Conversion from Stage 1)
Stage 3: KYC Completed [  36,000 ] ------ (60% Conversion from Stage 2)
Stage 4: Active Accounts[ 18,000 ] --- (50% Conversion from Stage 3)

• Stage-to-Stage Conversion Rate:
  $\text{Conversion \%} = \left( \frac{\text{Volume in Stage } k}{\text{Volume in Stage } k-1} \right) \times 100$
• Overall Pipeline Conversion Rate:
  $\text{Overall Conversion \%} = \left( \frac{\text{Volume in Final Stage}}{\text{Volume in Initial Stage}} \right) \times 100$

Scatter Plots (Bivariate Data Distributions)

Scatter plots display individual data points plotted on Cartesian coordinates $(X, Y)$, such as Interest Rate ($X$) vs. Loan Default Rate ($Y$).

• Positive Correlation: Data points trend upward from left to right.
• Negative Correlation: Data points trend downward from left to right.
• Outliers: Isolated points situated far from the primary cluster trendline.

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4. Realistic Worked Example 1: Profit & Loss DI Set

Data Set Description: A table provides pricing details for 4 banking investment products.

Problem 1: Profit Percentage of Product Alpha

Question: What is the Profit Percentage earned on Product Alpha?

Step-by-step Solution:

1. Cost Price (CP) $= ₹5,000$
2. Marked Price (MP) $= 5,000 \times (1 + 0.40) = 5,000 \times 1.40 = ₹7,000$
3. Selling Price (SP) $= 7,000 \times (1 - 0.15) = 7,000 \times 0.85 = ₹5,950$
4. Profit Amount $= \text{SP} - \text{CP} = 5,950 - 5,000 = ₹950$
5. Profit Percentage $= \left( \frac{950}{5,000} \right) \times 100 = 19.0%$

Problem 2: Cost Price of Product Beta

Question: If the Selling Price of Product Beta is ₹7,200, find its Cost Price.

Step-by-step Solution:

1. Given Profit $= 20% \implies \text{SP} = 1.20 \times \text{CP}$
2. $7,200 = 1.20 \times \text{CP} \implies \text{CP} = \frac{7,200}{1.20} = ₹6,000$

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5. Realistic Worked Example 2: Digital Loan Funnel DI Set

Data Set Description: SBI digital loan application funnel with an initial top-stage volume of $200,000$ initial applications:

• Stage 1 (Application Received): $200,000$
• Stage 2 (Document Verification): $65%$ conversion from Stage 1
• Stage 3 (Credit Audit Approval): $80%$ conversion from Stage 2
• Stage 4 (Loan Sanctioned): $75%$ conversion from Stage 3
• Stage 5 (Loan Disbursed): $90%$ conversion from Stage 4

Problem: Disbursed Loan Volume & Overall Conversion

Question: How many loans were ultimately disbursed (Stage 5), and what is the overall funnel conversion percentage?

Step-by-step Solution:

1. Stage 2 Volume $= 200,000 \times 0.65 = 130,000$
2. Stage 3 Volume $= 130,000 \times 0.80 = 104,000$
3. Stage 4 Volume $= 104,000 \times 0.75 = 78,000$
4. Stage 5 Disbursed Volume $= 78,000 \times 0.90 = 70,200\text{ loans}$
5. Overall Conversion Rate:
   $\text{Overall Conversion} = \left( \frac{70,200}{200,000} \right) \times 100 = 35.1\%$

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6. Strategic Mastery for Mains Arithmetic DI

1. Formula Verification: Write down fundamental arithmetic formulas on your scratch sheet before solving complex sets.
2. Track Intermediate Steps: In multi-stage Funnel charts, avoid rounding intermediate values; calculate cumulative product multipliers (Base * p1 * p2 * p3) in a single continuous calculation.
3. Scatter Plot Axis Scale Alignment: Carefully check grid unit steps on both X and Y axes to prevent incorrect point coordinate readings.