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Maths · Quantitative Aptitude

Arithmetic Core

Arithmetic carries the maximum weight in SSC, RRB Group D, NTPC, Banking and Insurance exams — typically 12–18 marks. The seven core sub-topics below (Percentage, Profit & Loss, Ratio, Average, Time & Work, Time-Speed-Distance, and Interes…
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Why it matters

RRB Group D / NTPC: 8–12 questions out of 25 are pure arithmetic. SSC CGL Tier-I: 6–8 questions. Bank PO/Clerk: 5–10 questions in Quant + Data Sufficiency.
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Percentage

A percentage is a ratio expressed out of 100; x% = x/100.

Exam tipWhen a value increases by x% and then decreases by x%, the result is always less than the original — by x²/100 percent.
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Profit & Loss (CP, SP, Discount, Markup)

Cost Price (CP) is what the seller pays; Selling Price (SP) is what the customer pays; Marked Price (MP) is the labelled price before discount.

Exam tipAlways express profit/loss as a percentage of CP, never of SP. A common trap in MCQs is calculating against SP.
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Ratio & Proportion (Partnership, Ages)

A ratio compares two quantities of the same kind; a proportion is an equality of two ratios (a:b = c:d).

Exam tipIf 'a:b = c:d', cross-multiplying gives a×d = b×c. Use this to solve any one unknown directly.
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Average

Average = Sum of observations ÷ Number of observations.

Exam tipFor average speed of unequal distances at known speeds, use Total Distance / Total Time, not the harmonic-mean shortcut.
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Short Tricks

Memorise percentage-to-fraction conversions
Convert percentages to fractions for instant calculation: 12.5%=1/8, 16.66%=1/6, 20%=1/5, 25%=1/4, 33.33%=1/3, 50%=1/2, 66.67%=2/3, 75%=3/4.
Net % change for two successive changes
Net % = a + b + (a × b)/100, with + for increase and − for decrease.
Same SP, x% gain and x% loss → always loss
When two articles are sold at the same SP, one at x% profit and the other at x% loss, the net loss = x²/100 % of the total CP.
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Quick Revision Facts

  • x% of y = y% of x. Use this to flip awkward calculations.
  • Successive discounts of a% and b% = a + b − ab/100 (always less than a+b).
  • Profit% on SP can never exceed 100%; on CP it can.
  • Average speed = Total distance / Total time — always.
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Mathematics — Quantitative Aptitude
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