diff --git a/backend/local/local.go b/backend/local/local.go
index cd0cc3890..a6cf3f2eb 100644
--- a/backend/local/local.go
+++ b/backend/local/local.go
@@ -1650,12 +1650,13 @@ func (o *Object) Update(ctx context.Context, in io.Reader, src fs.ObjectInfo, op
 		out = nopWriterCloser{&symlinkData}
 	}
 
-	// Calculate the hash of the object we are reading as we go along
+	// Calculate the hash of the object as we write it
+	var w io.Writer = out
 	if hasher != nil {
-		in = io.TeeReader(in, hasher)
+		w = io.MultiWriter(w, hasher)
 	}
 
-	_, err = io.Copy(out, in)
+	_, err = io.Copy(w, in)
 	closeErr := out.Close()
 	if err == nil {
 		err = closeErr
diff --git a/backend/local/local_internal_test.go b/backend/local/local_internal_test.go
index 761aa8ea6..25adcdf80 100644
--- a/backend/local/local_internal_test.go
+++ b/backend/local/local_internal_test.go
@@ -499,6 +499,32 @@ func TestHashOnUpdate(t *testing.T) {
 	assert.Equal(t, "45685e95985e20822fb2538a522a5ccf", md5)
 }
 
+// Test the hash cached by Update matches a HashesOption hint passed by the caller
+func TestHashOnUpdateWithHashOption(t *testing.T) {
+	ctx := context.Background()
+	r := fstest.NewRun(t)
+	const filePath = "file.txt"
+	when := time.Now()
+	r.WriteFile(filePath, "x", when)
+	f := r.Flocal.(*Fs)
+
+	o, err := f.NewObject(ctx, filePath)
+	require.NoError(t, err)
+
+	b := bytes.NewBufferString("content")
+	src := object.NewStaticObjectInfo(filePath, when, int64(b.Len()), true, nil, f)
+	options := []fs.OpenOption{&fs.HashesOption{Hashes: hash.NewHashSet(hash.MD5)}}
+	require.NoError(t, o.Update(ctx, b, src, options...))
+
+	gotContent, err := os.ReadFile(filepath.Join(f.root, filePath))
+	require.NoError(t, err)
+	assert.Equal(t, "content", string(gotContent))
+
+	md5, err := o.Hash(ctx, hash.MD5)
+	require.NoError(t, err)
+	assert.Equal(t, "9a0364b9e99bb480dd25e1f0284c8555", md5)
+}
+
 // Test hashes on deleting an object
 func TestHashOnDelete(t *testing.T) {
 	ctx := context.Background()