The income of X is 20% more than that of Y, and the income of Y is 10% more than that of Z. If X’s income is ₹ 26,400, find the income of Z.
₹ 20,000
Successive percentage increases multiply: a rise of 10% multiplies by 1.1 and a rise of 20% multiplies by 1.2.
Step 1 — Let Z's income be z. Then Y = 1.1z and X = 1.2 × 1.1z = 1.32z.
Step 2 — \(1.32z = 26400 \Rightarrow z = \frac{26400}{1.32} = 20000\).
Step 3 — Check: Y = 1.1 × 20,000 = ₹ 22,000 and X = 1.2 × 22,000 = ₹ 26,400. ₹ 22,000 is Y's income, ₹ 24,000 undoes only the 10% step (26,400 ÷ 1.1), and ₹ 18,480 comes from subtracting 30% of ₹ 26,400 instead of dividing by 1.32.
₹ 20,000 option is correct.
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