A man sells a watch at a profit of 20%. If he had bought it at 10% less and sold it for Rs. 30 less, he would have gained 20%. Find the initial cost price. MCQ with Answer and Explanation

Explanation:
CP = 560 / 1.12 = 500.

Explanation:
SP = 105% of 400 = 420. Marked Price (MP) - 16% of MP = SP. 0.84 * MP = 420. MP = 420 / 0.84 = Rs. 500.

Explanation:
Let CP = x. Loss 5% => SP1 = 0.95x. If sold at gain 10%, SP2 = 1.1x. Given 1.1x - 0.95x = 100 => 0.15x = 100 => x = 100/0.15 = 666.67, not in options. Wait, recalc: Difference = 15% of CP = 100 => CP = 100/0.15 = 666.67. But options are whole. Perhaps 500? Test: 0.15*500=75 not 100. 700 gives 105, close. But exact not in options. Let's adjust: maybe the gain would have been 10% more? Actually the problem says: if sold for Rs. 100 more, he would have gained 10% instead of loss 5%. The difference in percentage points is 15%, so 15% of CP = 100 => CP = 666.67. Not an option. So this question is flawed. I'll delete and regenerate another easy question.