Two shops stock the same water purifier. Shop A has marked it ₹3200 and sells it at 25% off. Shop B has marked the same purifier ₹4000. What discount percent must Shop B allow if it is to sell at exactly Shop A's price?

Shop A sells at $3200\times 0.75$ = ₹2400, so Shop B must come down from ₹4000 to ₹2400 — a cut of ₹1600, which is 40% of ₹4000. (Matching A's RATE of 25% would leave B at ₹3000, still dearer; matching the ₹800 that A knocked off gives 800/4000 = 20% and leaves B at ₹3200. 50% measures B's required ₹1600 cut against A's ₹3200 marked price — the right cut, divided by the wrong shop's ticket.)