Commercial Mathematics, Quadratic Equations & Algebra (GST, Banking, Shares) — Practice

Question 1

A washing machine is sold for Rs 25,000 exclusive of GST. If the GST rate is 12%, find (a) the GST amount, (b) the final selling price. If the retailer had bought it for Rs 18,000 + GST, find his Input Tax Credit and the net GST he pays to the government.

Accepted Answer

GST on sale = 12% × 25,000 = Rs 3,000. Final price = 25,000 + 3,000 = Rs 28,000. GST paid on purchase (Input GST) = 12% × 18,000 = Rs 2,160. GST collected on sale (Output GST) = Rs 3,000. Net GST payable to government = Output GST − Input GST = 3,000 − 2,160 = Rs 840. (CGST = Rs 420, SGST = Rs 420 if intra-state.)

Question 2

Two taps can fill a tank together in 6 minutes. The larger tap takes 5 minutes less than the smaller tap to fill the tank alone. Find the time each tap takes alone.

Accepted Answer

Let smaller tap take x minutes alone. Larger tap takes (x−5) minutes. In 1 minute: smaller does 1/x, larger does 1/(x−5), together: 1/6. So 1/x + 1/(x−5) = 1/6. Multiply through by 6x(x−5): 6(x−5) + 6x = x(x−5). 6x − 30 + 6x = x² − 5x. 12x − 30 = x² − 5x. x² − 17x + 30 = 0. Factoring: (x−15)(x−2) = 0. x = 15 or x = 2. If x = 2, larger tap = −3 min (impossible). REJECT x = 2. Answer: Smaller tap = 15 minutes, Larger tap = 10 minutes. Check: 1/15 + 1/10 = 2/30 + 3/30 = 5/30 = 1/6 ✓.

Question 3

A man has a choice of investing Rs 72,000 in either (i) 16% Rs 100 shares at Rs 120 or (ii) 14% Rs 100 shares at Rs 105. Find which investment gives a better return and by how much (as %).

Accepted Answer

Investment (i): 16% Rs 100 shares at Rs 120. No. of shares = 72,000 / 120 = 600. Annual dividend = 600 × 16% × 100 = Rs 9,600. Return % = (9,600 / 72,000) × 100 = 13.33%. Investment (ii): 14% Rs 100 shares at Rs 105. No. of shares = 72,000 / 105 = 685.71 (take 685 shares). Investment = 685 × 105 = Rs 71,925. Annual dividend = 685 × 14% × 100 = Rs 9,590. Return % = (9,590 / 71,925) × 100 ≈ 13.33%. [Or use formula: Return% = (d × FV) / MP. (i) = 16×100/120 = 13.33%. (ii) = 14×100/105 = 13.33%.] Both give equal returns. [Examiners often phrase the numbers so one is clearly better — use the formula Return% = (dividend% × FV) / MP for a fast comparison.]

Practice — Commercial Mathematics, Quadratic Equations & Algebra (GST, Banking, Shares)

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