a new owner of a diahatsue sportrax in need of help

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hello i ave recently bought my diahatsue sportrax 1.6 manual injection an it start purfect but after 10-15 mins it cuts out and splutters and wont start again for 5-10 mins its not raising in temputure and stinking of petrol ive asked about and theve cum up with spark plugs/leads/coil pack auto choke is sticking or kompresson in the engine isent right when the car cuts out if you try and start it straight away it just turns over an little puffs of dark smoke from exhaust comes out.please let me no what u think thanks simon

Try ........

Where do we start!
Check if there is coolant in the radiator and expansion tank.
Check the back-end of the fuel tank .... any signs of leaking petrol?
After 10 minutes running the temp gauge should be 'up' at normal. No reading .. has the temp gauge been disconnected?
Is the air filter blocked? Remove the filter and run/try without a filter. Replace with a new filter if car runs beyond the 15 minutes.
Choke stuck? Remove air filter. Start the engine and raise the revs. Pour/drip REDEX into the air intake. Let the engine turn over for a minute. Then rev hard and 'crap' will be ejected from the inlets.
Also with filter removed raise the revs. Jamb a clean cotton cloth over the intake to create suckion - dont let the cloth get sucked into the air intake. The vacuum will suck and unblocked the carbs jets.

Failing that you need to buy a friendly DIY mechanic a good drink and ask for help! The problem could prove very expensive.

In Addition

In addition to mace's post, try swapping the coil, if it is beginning to break down it will give these symptoms. As it works it heats up, when it reaches a certain temperature it breaks down, leaving it for several minutes allows it to cool down again, so it works until it heats up again.

The petrol smell is the unburnt fuel passing through the conbustion chambers, this washes the oil from the cylinder walls and gives the black smoke.