Arithmetic: Numbers, Ratio and Financial Computation
Arithmetic supplies the computation that underlies both papers: prime factorisation, ratio and percentage, and the commercial arithmetic of GST and shares. These questions are short but unforgiving of a single arithmetic slip, so keep the working visible.
HCF, LCM and numbers
Prime factorise each number. The HCF takes the lowest power of every prime common to all the numbers; the LCM takes the highest power of every prime that appears. For two numbers only, HCF × LCM = product of the numbers; this rule does not extend to three numbers.
Ratio and percentage
A ratio a : b compares quantities in the same unit. When a : b = 2 : 3, write the parts as 2x and 3x and solve for x, rather than guessing values. Percentage change = (change ÷ original) × 100, always divided by the original quantity, and simple interest is I = PRN/100.
GST
For an intra-State supply, GST = CGST + SGST, each being half of the total rate. The bill amount equals taxable value plus GST. Input tax credit is set off against the output tax payable.
Shares
Number of shares = investment ÷ market value. Annual dividend = number of shares × face value × rate of dividend. Rate of return = (dividend per share ÷ market value) × 100, so a share bought above face value yields less than its declared rate.
Worked example
A taxable value of ₹2,500 attracts 18% GST within the State. CGST = 9% of 2,500 = ₹225 and SGST = ₹225, so total GST = ₹450 and the bill is ₹2,500 + ₹450 = ₹2,950.
Traps that cost marks
Charging 18% as CGST and again as SGST doubles the tax. Dividing percentage change by the new value instead of the original, mixing units in a ratio, applying HCF × LCM to three numbers, and using face value where market value is required are the other frequent losses.