Price decreased by 15% then increased by 15%. Net change is: MCQ with Answer and Explanation

Explanation:
1.3 × x = 1.05 → x = 1.05/1.3 ≈ 0.8077, reduction 19.23%.

Explanation:
Speak at least one = 100% - 27% = 73%. n(E U H) = n(E) + n(H) - n(E ∩ H). 73 = 70 + 65 - n(E ∩ H). n(E ∩ H) = 135 - 73 = 62%.

Explanation:
CP=x, SP=1.12x. New CP=0.88x, new SP=1.12x+12, new SP=1.25×0.88x=1.1x. So 1.12x+12=1.1x → 0.02x= -12 impossible. So adjust: let SP at 15% profit, bought at 10% less, sold for Rs. 15 more, gain 20%. CP=x, SP=1.15x. New CP=0.9x, new SP=1.15x+15=1.2×0.9x=1.08x → 1.15x+15=1.08x → 0.07x= -15 no. Need right: gain more when bought cheaper and sold higher. So if bought cheaper and sold higher, profit% should be more than original. So CP=x, SP=1.1x (10% profit). Bought at 20% less (0.8x), sold for Rs. 10 more (1.1x+10), gain 30% → 1.1x+10 = 1.3×0.8x = 1.04x → 0.06x= -10 no. Let original profit 10%, CP=x, SP=1.1x. Bought at 20% less (0.8x), sold for Rs. 20 more (1.1x+20), gain 30% → 1.1x+20=1.04x → negative. So the correct pattern: bought at 20% less, sold at same SP gives higher profit%. To get gain 25% on new CP, new SP = 1.25×0.8x = x. But original SP is higher. So if original SP is 1.1x, and new SP is x, then it's less, so sold for less. So phrase: if sold for Rs. 10 less. So: CP=x, SP=1.1x. Bought at 20% less (0.8x), sold for Rs. 10 less (1.1x-10), gain 25% → 1.1x-10 = 1.25×0.8x = x → 0.1x=10 → x=100. So CP=100. I'll use: sells at 10% profit, if bought 20% less, sold for Rs.10 less, gain 25%. CP=100. Good.