这样的方法应该有用：

SELECT CASE WHEN b.amount < 10 THEN '0-10'
  WHEN b.amount < 20 THEN '11-20'
  WHEN b.amount < 30 THEN '21-30'
  WHEN b.amount < 40 THEN '31-40'
  WHEN b.amount < 50 THEN '41-50'
  ELSE '50 and more' END AS total_amount,
  count(DISTINCT b.user_id) AS number_of_users 
FROM activity a
JOIN payments b
ON a.user_id = b.user_id
WHERE a.login_time = '2018-04-18'
GROUP BY 1

如果在活动表中，用户每天只能出现一次，则可以使用count（*）而不是count（不同的用户标识）。
希望有帮助

和内部连接时的用例

select case when amount<=10 then '0-10' when amount>10 and amount<20 then '10-20'
when amount>=30 and amount<50 then '30-50'
when amount>=50 then '50-and more' end as total_amount,count(payments.user_id)
from payments inner join activity on payments.user_id=activity.user_id
where login_time='2018-04-20'
group by case when amount<=10 then '0-10' when amount>10 and amount<20 then '10-20'
when amount>=30 and amount<50 then '30-50'
when amount>=50 then '50-and more' end