How to increase mobile app rank in playstore without using money.

To get top ranking in Google play store follow these tips:
Optimize Google play store page with keywords
Check your site for 0% errors
Great keywords boost your app.
Go for social media to popular app
Get ratings and reviews
Optimize content with keywords

App can also rank in search results so i think you have to promote the app in different related websites which are trusted in the related field.

App Store Keyword Optimization
Use all 100 characters.
Separate every keyword by a comma.
Avoid space, articles and prepositions.
Use singular OR plural, the easier one to rank for.
Don't repeat keyword.
Use numbers instead of spelled out words.

One of the best ways to get more reviews and ratings is by encouraging feedback and interaction with the users.

App Store is a platform to download and install applications for devices. It lists and prioritizes the number of applications on the basis of multiple factors. You should have to follow these below some factors to rank your app,
• Content and description of the product according to keyword
• User feedback
• Reviews
• Ratings
• Add in-app purchases information

Use App store keyword optimization, add ratings & reviews for better ranking.

To increase app rank, App store optimization (ASO) factor must pay attention on these factors:
App name and title
Keywords
Description
Subtitle
Total number of downloads
Rating and reviews

To increase app rank, you must increase your viewers, downloader and increase your rating.