Most people can no longer make a new claim for tax credits because it has been replaced with Universal Credit (unless very limited circumstances apply). The rest of this article is only relevant if you have an existing Tax Credit claim.
They are both based on your income, and worked out in one calculation. WTC and CTC are both administered by the Tax Credit Office, part of HMRC.
You may qualify for just CTC, just WTC, both together, or neither, but both use the same form and an application for one is an application for both.
Single people must claim on their own whereas couples who live together must claim as a couple, with both their incomes taken into account. However, in general, you cannot make new claims for Tax Credits.
Your Tax Credit award is worked out by calculating a maximum possible award for your circumstances, made up of all the elements you are eligible for. Your income (based on either the previous tax year or an estimate of the current tax year) is then worked out and the maximum is reduced to give the amount you are entitled to receive. You can find more information on how tax credits are worked out from the Low Incomes Tax Reform Group.
There is lots more information about tax credits on the GOV.UK website.
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