Key facts

  • Profit or loss is always compared with cost price unless the question clearly gives another base; profit percentage = profit x 100 / cost price.
  • Simple interest uses interest on the original principal only: SI = P x R x T / 100, and amount = principal + interest.
  • Compound interest adds interest to the principal at each compounding step; for annual compounding, amount = P(1 + R/100)^T.

Key Points at a Glance

  1. 1

    HCF gives the greatest common divisor for exact equal grouping; LCM gives the least common multiple for first common repetition or the minimum quantity divisible by several numbers.

  2. 2

    Average = sum of observations divided by number of observations; in exam questions, watch for added, removed, or replaced observations before using a direct formula.

  3. 3

    Profit or loss is always compared with cost price unless the question clearly gives another base; profit percentage = profit x 100 / cost price.

  4. 4

    Percentage means per hundred; percentage points and percentage change are different, so always identify the original base.

  5. 5

    Simple interest uses interest on the original principal only: SI = P x R x T / 100, and amount = principal + interest.

  6. 6

    Compound interest adds interest to the principal at each compounding step; for annual compounding, amount = P(1 + R/100)^T.

  7. 7

    Ratio compares quantities in the same unit; proportion states equality of two ratios, and the product of extremes equals the product of means.

  8. 8

    Before applying any formula, make units common: months to years, hours to minutes, kilograms to grams, and rupees/paise to one unit.

CET Senior Secondary study hubView study packs

LCM and HCF: Where Each One Fits

HCF, or highest common factor, is the greatest positive integer that divides all given numbers exactly. It is useful when a question asks for the greatest equal size, greatest equal length, largest identical packet, or maximum number that can divide several quantities without a remainder. For example, the greatest length that can exactly cut 84 m and 126 m ropes is HCF(84, 126) = 42 m. By prime factorisation, take the common prime factors with the smallest powers; by division method, keep dividing by the remainder until the remainder becomes 0.

LCM, or least common multiple, is the smallest positive integer divisible by all given numbers. It is useful when a question asks for the first time together, least common quantity, repeated cycles, bells ringing together, or a minimum number divisible by several divisors. For example, events repeating every 12, 15, and 20 seconds meet again after LCM(12, 15, 20) = 60 seconds.

For two positive integers a and b, HCF(a, b) x LCM(a, b) = a x b. Use this relation only for two positive integers, not blindly for three numbers or fractions.

Open the complete note

This public page shows the first available section. The study pack opens the complete topic with all revision material.

7 more sections in the complete note

Open study pack