A bought a cycle and sold it to B at a profit of ₹1,000. B sold it to C at 5% loss. C sold it to D for ₹10,450 at 10% profit. If D had bought the cycle directly from where A had bought, then how much amount (in ₹) would he have saved?

Let's work backwards from D's purchasing price to find the original cost price for A.
Step 1: Find C's cost price (or selling price to D)
C sold it to D at a 10% profit for ₹10,450.

Cost Price for C×1.10=10,450
Cost Price for C=
1.10
10,450
​
=9,500
Step 2: Find B's cost price (or selling price to C)
B sold it to C at a 5% loss.

Cost Price for B×0.95=9,500
Cost Price for B=
0.95
9,500
​
=10,000
Step 3: Find A's cost price
A sold it to B at a flat profit of ₹1,000.

Cost Price for A+1,000=Cost Price for B
Cost Price for A+1,000=10,000⟹Cost Price for A=9,000
Step 4: Calculate savings for D
If D bought it directly from where A bought it, D would pay A's cost price (₹9,000).

Savings=Price paid by D−Cost Price for A
Savings=10,450−9,000=1,450