currency forward rate question

I dont’ undersatnd I thought formula was F=S x (1+Rd)/(1+Rf) How is the price basket here 1/2 and not 2/1. If its 1.5 dollars per pounds, isn’t it 1.6*(2*1.06)/(1*1.11) and not the way its done in the answer? Is this answer wrong?

A U.S. investor purchased a U.K. bond one year ago. The exchange rate at the time was 1.6 to 1 (dollars to pounds) and the beginning-of-period ratio of the price levels of the consumption baskets was 2 ($ to £). During the year, inflation in the U.S. was 6% and in the U.K. was 11%. Today the exchange rate is 1.7. Which of the following is closest to the end-of-period real exchange rate?

A) 0.890. B) 1.123. C) 1.005.

Your answer: B was incorrect. The correct answer was A) 0.890.

The end-of-period real exchange rate is calculated as: X = S (PF/PD). Here, the new price levels are 1.11 for the U.K. (1 × 1.11 = 1.11) and 2.12 for the U.S. (2 × 1.06 = 2.12). Hence, the end-of-period real rate is 0.890 [= X = S (PF/PD) = 1.7 (1.11 / 2.12)].

This example seems to have nothing to do with currency forward rates; instead, it’s asking you to calculate the real exchange rate. The formula for calculating real exchange rates is: Real S= Nominal S x (PF/PD), where S is quoted per unit of FC (i.e., FC:DC). This can be confusing because the denominator and the numerator are reversed from what we’re used to seeing elsewhere.

Personally, I prefer to think of this equation in this alternative form: Nominal S = Real S x (PD/PF). The intuition would be that if Real S = 1, Nominal S (i.e., DC/FC) would be equal to PD/PF. (e.g., if the Big Mac costs 1.40 USD in the U.S. and 1.00 EUR in Europe and Real S is currently 1 (i.e., PPP holds), then Nominal S should be 1.40 USD per EUR.)