A shopkeeper cut the price by 20%. To bring it back to the old price, he raises that reduced price…

Why

Ravi's using 'down 20, up 20, so even' — but the two 20%s are slices of DIFFERENT prices, so they aren't equal in rupees. Take Rs 100: cut 20% and it's Rs 80. Now raise THAT by 20% — but 20% of 80 is only Rs 16, giving Rs 96, still short of 100. The rise was figured on the smaller Rs 80, so it adds back less than the cut removed from the larger Rs 100. Same percent, smaller base, smaller effect. To truly restore Rs 100 from Rs 80 he'd need a 25% rise, not 20. Test: this is why 'discount then same-percent markup' never lands back home — the markup works on a shrunk number. Ravi's not right: it's still lower (Rs 96 on 100), because the 20% rise came off a smaller price than the 20% cut did.