Both have different engines.
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Our cuore L500 came with ED-10 engine.....also it came with ED-20, EF-CL, EF-JL and JB series engine but not in our market.
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The Mira L250 came with EF-SE engine in our market mostly....there are few of em with EJ-VE or EJ-DE too whch were 1000cc
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I would suggest to change ur mechanic if he suggest engine change because he cant do overhaul and has incorrect engine info.
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What's the total mileage of ur car and what oil were u using?
Oil burn is not that big issue and can be resolved with overhaul.... unfortunately i cannot tell about wrkshop fr good work but others here can if u share ur city/location
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Also note the engine EF-SE and EJ-VE/EJ are hard to find....let alone good condition coz they were produced between 02-06