Lease and sale back

This question is from ACCA practice paper 1:
Agreement 3:
This sale and leaseback relates to a cutting machine purchased by
Blocks Co on 1 January 20X4 for $300,000. The carrying amount of the
machine as at 31 December 20X4 was $250,000. On 1 January 20X5,
it was sold to Cogs Co for $370,000, the fair value of the asset was
$320,000, and Blocks Co will lease the machine back for five years,
The sale meets the revenue recognition requirements of IFRS 15
Revenue from Contracts with Customers. The financial liability is
measured at S300.000 on 1 January 20X5, of which $50,000 relates to
the additional financing.
For agreement three, what profit should be recognised for the year ended 31 December 20X5 as a result of the sale and leaseback (to the nearest whole $)?
Sample solution:
The profit to be recognised is based on the rights transferred to
the lessor
Gain x ((Fair value of asset – lease liability) / Fair value of asset)
70,000 x ((320,000 – 250,000) / 320,000)
70,000 x 0.21875
$15,312.50
Accept $15,312 and $15,313

My problem is why are there using the purchase price to calculate gain shouldn’t they be using the carry amount.
Gain according to me = selling price – carry amount = 370000-250000 = 120000
Why is their gain 70000 (they are probably doing 370000-300000 but why?)