A160 elegance model 2001 5 door hatch back,gear not changing goes upto 60 km, it shows 5-6 rpm range if speed is increased

They have a problem with the froward gear brake drums cracking and there is a replacement/updated drum available but you would need an auto trans repairer to rebuild the transmission.

Disclaimer - beware - these little cars are very complex and easy to destroy computers.

1st option: No details re history so will assume it is in limp mode only driving in 2nd or reverse?
If so check fluid level in gearbox when hot -run for 20 minutes in driveway should do the trick. Find sealed filler hose and insert aftermarket dipstick. (There are youtube videos on how to make DIY one out of curtain spring wire) If level alright it will be valve body grunge and needs expert auto to clean. Otherwise add EXACTLY 500ml of synthetic fluid from Mercedes. try operating after heating gearbox as before. If good get auto serviced.

2nd option: Operate emergency Park release if Gear change not moving. remove gear change module cover and check connections in circuit board.
Very good website called Lofty's A160 page for DIYER's

Its probably not trans. More than likely its coming from a ring/pinion. Normal wear and tear will cause a slight excess increase in play producing a gear whine. One way to reduce it is to use a thicker gear oil. 85-140 weight should reduce or eliminate at.

check around gear box repair shops to see if there is a replacement box that has an overdrive gear (5th)
if it is an automatic , the problem may be that overdrive is not coming in and that will drop the rpm 250 rpm and increase the speed up to the 75 mph mark
there is nothing wrong in the box as the rpm and the speed are about right in relation to the diff ratio(not mentioned )
3200 rpm with a overdrive manual runs around 74 mph or 120 km/hr
another method is to put a diff in with a taller ratio
example --current 4.1 back to 3.2

their are 5 different 5 models performance is from the highest hp motor Renault 5 Alpine
5 model for Europe , 3-door hatchback with manual 5-speed and 1397 cm3 / 68 kW (91 hp / 92 PS); Top speed: 173 km/h / 108 mph 0-60 mph (s): 9.5 0-100 km/h (s): 10.1 http://www.automobile-catalog.com/

TPS (Throttle posision sensor) would be my guess

change trans fluid and filter and a fuel filter might not hert

one unit that operates ratio changes and is connected to the engine is that vacuum operated actuator on the transmission
it is possible that that unit is failing , vacuum hose is leaking and that will cause ratio changes as the vacuum varies
run the fault codes to check for wiring problems or VSS or TCM problems as well

Hyundai grandeur was running fine and now simply wont start. it turns over fine but thats it?