Maharashtra SSC Arithmetic (MSBSHSE) common mistakes
Maharashtra SSC Arithmetic (MSBSHSE) · Understand the traps and how to avoid them.
When subtracting a negative integer, the candidate changes the sign of the first number instead of the second, e.g. writing 7 − (−3) = 4 by treating it as 7 − 3, or computing −5 − 8 as −5 + 8 = 3.
The rule 'minus minus makes plus' is memorised as a phrase but not attached to the subtrahend, so under time pressure the sign flip lands on the wrong term. Textbook examples usually have the negative number second, so the pattern is fragile when the order changes.
What to do instead
Rewrite every subtraction as addition before computing: a − b means a + (−b). Practise ten mixed items such as −5 − 8 → −5 + (−8) = −13 and 7 − (−3) → 7 + 3 = 10. Say the rewritten line aloud before evaluating, and check the answer against a number line for the first week.
In fraction arithmetic the candidate adds numerators and denominators straight across, e.g. 2/3 + 1/4 = 3/7, or multiplies without cross-cancelling and then mis-simplifies the result.
Whole-number addition is additive over parts, and the visual similarity of the fraction notation invites the same move. Students who never built the 'common denominator means same-sized pieces' idea fall back on the whole-number rule.
What to do instead
Force the intermediate step: write each fraction with an explicit LCM denominator before adding (2/3 = 8/12, 1/4 = 3/12, sum 11/12). For multiplication, cancel common factors first and write the cancelled pair. Do five items daily where the answer must be shown in lowest terms with the HCF stated.
The candidate sets up a proportion with the terms in the wrong order, e.g. writing 5 pens : ₹40 = 8 pens : x but solving 5/40 = x/8, or in inverse variation uses the direct-variation cross-multiplication.
The rule 'product of means equals product of extremes' is applied mechanically without checking which quantity is paired with which. Inverse variation is taught as a formula rather than as 'one goes up, the other goes down', so the direction of the relationship is never inspected.
What to do instead
Before solving, write a labelled table with units in each column and an arrow showing whether the unknown should be larger or smaller. If larger, use direct proportion (a/b = c/d); if smaller, use inverse (a × b = c × d). Check the answer against the arrow - a result pointing the wrong way signals a flipped setup.
Percentage change is computed against the new value or against the wrong base, e.g. a price rising from 80 to 100 is reported as a 20% increase because 20/100 is used, or successive discounts of 10% and 10% are combined as a single 20% discount.
The phrase 'per cent' is read as 'divide by the number you have' rather than 'divide by the original'. Successive percentage changes feel additive because the two rates are added in everyday speech.
What to do instead
Always write the base explicitly: change/original × 100, with the original value circled. For successive changes, use the multiplier method - 0.9 × 0.9 = 0.81, i.e. an 19% total discount, not 20%. Drill five successive-change items and require the multiplier product to be shown.
Profit or loss percent is calculated on the selling price instead of the cost price, or the candidate confuses profit percent with profit in rupees when both cost and selling price are given.
The formula is remembered as 'profit over the other number' without the anchor that CP is always the base. When SP is larger and more prominent in the question, it is grabbed as the denominator.
What to do instead
Write the identity CP + profit = SP at the top of every solution and label which value is the base before dividing. Compute profit percent = (SP − CP)/CP × 100 with CP underlined. Include reverse problems (given SP and profit %, find CP) so the base is identified from the unknown side too.
In compound interest the candidate applies simple interest for the whole period, or uses the rate per annum directly for a half-yearly or quarterly compounding period without adjusting rate and time.
SI and CI formulas look nearly identical and both use P, R, T. Half-yearly compounding adds a second layer (halve the rate, double the periods) that is often skipped because the question still quotes an annual rate.
What to do instead
Build a habit of writing the compounding schedule: for half-yearly, R/2 per half-year and 2T periods; for quarterly, R/4 and 4T. Compute year by year for two-year problems to see the difference from SI, then verify with A = P(1 + R/100)^n. Always state n and the per-period rate before substituting.
Area and volume formulas are swapped or the wrong dimension is squared: the candidate uses 2πr for the area of a circle, uses 4/3πr² for a sphere volume, or computes the surface area of a cylinder as πr²h.
Formulas are memorised as strings of symbols without a dimensional check. Because πr² and 2πr both contain r and π, they blur together, and volume versus surface area is not linked to units (square versus cubic).
What to do instead
Attach units to every formula: area answers in cm², volume in cm³, and reject any result whose unit does not match the question. Keep a one-page formula card with a sketch beside each formula, and do mixed sets where the same radius is used for circumference, area, and volume so the differences are visible.
Unit conversion is skipped before substituting into a formula, e.g. a rectangle given as 1.5 m by 40 cm is multiplied as 1.5 × 40, or litres are substituted where cubic centimetres are needed.
Numbers are copied into the formula as they appear in the question. Students do not habitually scan for mixed units, and the 1 litre = 1000 cm³ link is recalled only when a conversion question is explicitly asked.
What to do instead
Make 'convert to one unit' the first written line of every measurement solution, before the formula. Maintain the conversion facts 1 m = 100 cm, 1 litre = 1000 cm³, 1 m³ = 10⁶ cm³ and apply them in drill items that deliberately mix metres and centimetres.
The candidate computes the mean correctly but reports the median of an unarranged list, or confuses mean, median, and mode when the question asks for a specific one, especially with an even number of observations.
Median is defined as the middle value, and the middle of the written list looks like the middle of the data. With an even count, the average of the two central values is a step that is easily dropped, and the three averages are taught together so their labels blur.
What to do instead
Always rewrite the data in ascending order before touching median or mode, and count the terms explicitly. For even n, write the two central positions (n/2 and n/2 + 1) and average them. Before answering, restate in one line what the question asks for and circle that word in the question.
When reading a bar graph or pie chart, the candidate reads the height of a bar as the value without using the scale, or converts a pie-chart sector to a quantity using 100 instead of 360 degrees.
The scale on the axis (for example 1 cm = 20 units) is treated as decoration, and pie charts are mentally converted as percentages because percentages are more familiar than degrees. The link between angle, fraction, and total is not practised.
What to do instead
Write the scale as a ratio on the first line (1 unit of height = k items) and multiply every reading by it. For pie charts, convert each sector with angle/360 × total, and cross-check that all sectors sum to the total or to 360°. Practise two graph-reading items per session with the scale deliberately not equal to 1.